5253:
3606:
5248:{\displaystyle {\begin{array}{l}f\times f=\sum _{j=0}^{\infty }{x^{j}/j!}\times \sum _{k=0}^{\infty }{y^{k}/k!}\\\\=\left\{{\begin{array}{cc}1&\times (1+y+y^{2}/2+y^{3}/3!+\dots )\\+x&\times (1+y+y^{2}/2+y^{3}/3!+\dots )\\+x^{2}/2&\times (1+y+y^{2}/2+y^{3}/3!+\dots )\\+\dots \end{array}}\right.\\\\=\left\{{\begin{array}{ccccccc}1&+y/1!&+y^{2}/2!&+y^{3}/3!&+y^{4}/4!&+y^{n}/n!&+\dots \\+x/1!&+xy&+{\frac {xy^{2}}{1!2!}}&+{\frac {xy^{3}}{1!3!}}&+{\frac {x^{n-4}y^{4}}{(n-4)!4!}}&+\dots &+\dots \\+x^{2}/2!&+{\frac {x^{2}y}{2!1!}}&+{\frac {x^{2}y^{2}}{2!2!}}&+{\frac {x^{n-3}y^{3}}{(n-3)!3!}}&+\dots &+\dots &+\dots \\+x^{3}/3!&+{\frac {x^{3}y}{3!1!}}&+{\frac {x^{n-2}y^{2}}{(n-2)!2!}}&+\dots &+\dots &+\dots &+\dots \\+x^{4}/4!&+{\frac {x^{n-1}y}{(n-1)!1!}}&+\dots &+\dots &+\dots &+\dots &+\dots \\+x^{n}/n!&+\dots &+\dots &+\dots &+\dots &+\dots &+\dots \\+\dots &+\dots &+\dots &+\dots &+\dots &+\dots &+\dots \end{array}}\right.\\\\=\left\{{\begin{array}{ccccc}1\\&+(x+y)\\&&+{\frac {(x+y)^{2}}{2!}}\\&&&+{\frac {(x+y)^{n}}{n!}}\\&&&&+\dots \end{array}}\right.\\\\=\sum _{n=0}^{\infty }{(x+y)^{n}/n!}=f\end{array}}}
2267:
617:
2262:{\displaystyle {\begin{aligned}\exp x\cdot \exp y&=\lim _{n\to \infty }\left(1+{\frac {x}{n}}\right)^{n}\cdot \lim _{n\to \infty }\left(1+{\frac {y}{n}}\right)^{n}\\&=\lim _{n\to \infty }\left\\&=\lim _{n\to \infty }\left^{n}\\&=\lim _{n\to \infty }\left(1+{\frac {x+y}{n}}+{\frac {xy}{n^{2}}}\right)^{n}\\&=\lim _{n\to \infty }\sum _{k=0}^{n}{\binom {n}{k}}\left(1+{\frac {x+y}{n}}\right)^{n-k}\left({\frac {xy}{n^{2}}}\right)^{k}{\text{(Binomial theorem)}}\\&=\lim _{n\to \infty }\left\\&=\lim _{n\to \infty }\left(1+{\frac {x+y}{n}}\right)^{n}+\lim _{n\to \infty }\left\\&=\lim _{n\to \infty }\left(1+{\frac {x+y}{n}}\right)^{n}+\lim _{n\to \infty }\left({\frac {xy}{n^{2}}}\right)\left\\&=\exp(x+y)+0{\text{ (as}}\lim _{n\to \infty }{\frac {xy}{n^{2}}}=0)\\&=\exp(x+y)\\\end{aligned}}}
5471:. The article actually defines these things differently. The natural exponential is given by a series (or other equivalent characterization), whereas exponential functions are given by approximation. This schizoid nature of the article makes it very confusing. The lede is five paragraphs long, for example. To me, that's an indication that there are really two different topics here: "Elementary" exponential functions, like those of precalculus, which can be rigorously defined using only integer exponentiation, continuity, and and completeness, and the natural exponential and those derived from it. Unfortunately, there is no distinction in usage between these two topics because the "natural" exponential is strictly more general.
279:, etc. tends to clutter, especially when there are parens around the whole term for one reason or another. However, having looked over quite a few math articles, my general feeling is that there are a lot (although I wouldn't automatically say most, or even a majority) of editors who include them. I'm not sure if this is because it's just their preference, or because they think it's required, or maybe for other reasons. Anyway, I'd be in favor of removing them when they're not necessary. For example, it would be necessary in an expression like
95:
85:
64:
31:
5590:
176:
2998:
22:
424:
405:
The equations y = e^(-kx) and y = 1-e^(-kx) are extremely common in engineering and physics, but I can't find a non-specific name for k or 1/k. In electronics 1/k is a time constant like "the RC time constant". In physics k can be called attenuation coefficient and 1/k can be the attenuation length.
5585:
I'm an old geographic scientist with broad mathematical experience and it seems to me that
Knowledge (XXG) doesn't make clear distinctions among the above concepts - any maybe some others as well. My own approach would be clear formulas and clear graphics - on the order of the thumbnail. Let me know
2774:
I think to improve coverage the article should have some discussion about branches. Maybe the exponential function as commonly defined is only one branch, but several related functions are inescapably branched and in some contexts it's convenient to consider the exponential function as a branched
2753:
Cosine and sine do not satisfy that identity, you may be thinking of the complex exponential, which can be expressed in terms of cosine and sine. Furthermore, a function is exponential if it is proportional to its rate of growth, so your equation is missing a constant factor.
406:
If you change e to 2, 1/k it is called the half-life. I think I've seen 1/k called the expected or mean life, time, or distance. Can someone think of what it is supposed to be called and include it in this article? 1/k is the "expected value" but that's too general.
2391:
Your proof is also incorrect (although fixable) and omits a couple things even still. I leave it as an exercise to determine where the mistake is, and also as a cautionary tale about coming up with your own proofs rather than adapting ones from existing sources.
3010:
5725:
A much harder point (but important for you - and for me as well) is how to get the whole WPen accept unique names in all eight cases? Short, but very artificial and therefore chanceless, should be: s-s-functions, a-a-functions, s-r-functions,
3285:
5503:
as defined by power series, infinite product, or differential equation. I think that the present article should mention but not go too deeply into the fact that the exponential function has an interpretation in terms of exponentiation:
5326:
By the way, the largest terms in e^m are the mth and (m-1)th terms, the others falling away in a
Gaussian like distribution with width square-root m. Throw in a factor like 2.2 and I think this may be related to Stirling's formula for
5731:
About sources. It's hardly to believe that this simple scheme shouldn't be ever mentioned on WPen. Or on other WPs, or other internet-pages. Half of the scheme - the four 'subtypes' - has a famous source, 200 years old: C-A Cauchy,
609:
531:
5855:-2. Isn't mathematical more just to use a defining condition, than to 'define' a class of functions by showing the form in which they are usually notated on paper? (In many cases several different forms are in use.)
3599:
3484:
3384:
151:
3125:
2287:
Again, this proof in not useful without a proof of the equivalence of the definitions. If one has the equivalence, one can use the definition through derivatives: The derivative with respect to
622:
5976:
3127:
the LHS is apparently assumed a priori (and proved later in the
Overview section). Perhaps for beginners it would be more satifying not to assume this but instead prove it by considering:
5652:
Your call for 'clear distinctions' brings me to the presentation of (not very well known?) verbal characterizations of four main types of functions, together with a subtype of each.
2855:
2975:
2775:
function as well. The article only vaguely hints at the branching behaviour and only if you already knew what to look for when you started reading (search for ‘multivalued’).
2337:
5966:
2585:
318:
379:
347:
2913:
2506:
5469:
2476:
2449:
2371:
3133:
35:
5981:
2377:. The proof takes only two lines and explains better why the identity is true. So, your proof is definitively not useful, except as an exercise for students.
5961:
2651:, instead of the other way around? With this in mind, perhaps an alternative lead could focus more on the key property of the exponential function, as in
5991:
141:
117:
5971:
536:
458:
5986:
3018:
5297:
I made some changes to the article including to address this concern. Rather than giving the proofs, I merely indicate that they exist. —
5351:
can be defined in several equivalent ways (by power series, infinite product, or differential equation) but it then has to be proved that
3492:
108:
69:
5754:
Please feel free to make concrete and specific suggestions about improvements you imagine to this or related articles. We have articles
2782:
2739:
2417:
2401:
390:
189:
2272:
5956:
5774:
but it could certainly be its own article. All of these could, like most articles in
Knowledge (XXG), benefit from more work. –
5570:
5426:
5311:
5272:
271:
touches briefly on this, but is certainly not definitive. Personally, I think having parentheses for standard functions like
44:
3392:
3292:
3052:
219:
4038:
5320:
Thank you for your changes addressing this concern. I could not spot them, but I may be looking in the wrong place.
249:
2692:
2588:
2545:
198:
50:
5803:, above 20/08) on defining a class of functions by their collective property, can be found in J. Dieudonné,
2786:
2743:
2718:
2513:
2397:
386:
5260:
2778:
237:
3022:
2670:
2539:
2276:
5335:
5268:
5476:
116:
on
Knowledge (XXG). If you would like to participate, please visit the project page, where you can join
5002:
94:
2808:
5755:
5330:
Hence 3 ways of looking at e^x - as well as the others mentioned in this article. Best wishes, Mike.
2982:
2977:. Obviously this is not true, but I wonder then how we should introduce these exponential functions.
2798:
2759:
2421:
5736:
1821, Chap.V, pp. 103-122. So maybe the other four types could be found in books from that period?
5331:
5264:
2918:
234:
Sometimes there's exp(z), sometimes there's exp z. Shouldn't an article be consistent with itself?
21:
5778:
5566:
5422:
5307:
2615:. Possibly the remainder of the article should also be restructured, but this is another question.
440:
5918:
5737:
5440:
I think part of the problem with this article is that it's really about two different things, the
2294:
451:
Correction to my edit to the
Overview section that got reverted (Forgot the binomial coefficients)
5937:
5288:
3001:
This article was the subject of a Wiki
Education Foundation-supported course assignment, between
2870:
2714:
2620:
2509:
2393:
2382:
382:
204:
100:
2612:
84:
63:
5695:(?) function transforms equiratio pairs into equidistant pairs: f(ru) - f(u) = f(rv) - f(v) .
5663:
function transforms equidistant pairs into equidistant pairs: f(u+s) - f(u) = f(v+s) - f(v) .
5323:
I wrote up these comments as it took me 60 years to spot that e^x was an 'a priori' assumption.
3280:{\displaystyle f\equiv \sum _{j=0}^{\infty }\;\;\;\;\;\;f\equiv \sum _{j=0}^{\infty }\equiv e.}
407:
282:
5922:
5741:
5602:
3034:
2701:
2597:
432:
5679:
function transforms equidistant pairs into equiratio pairs: f(u+s) / f(u) = f(v+s) / f(v) .
352:
5589:
5472:
323:
200:
175:
5512:. Likewise, I think it is appropriate to mention but not go too deeply into the fact that
2888:
2481:
5720:(?) function (R→R) transforms multiplications into multiplications f(uv) = f(u) · f(v) .
5447:
2978:
2802:
2755:
2611:
and to edit accordingly the remainder of the lead. This would be an implementation of the
2454:
2427:
2349:
5711:
function transforms equiratio pairs into equiratio pairs: f(ru) / f(u) = f(rv) / f(v) .
5775:
5771:
5767:
5759:
5557:
5487:
5413:
5298:
3014:
2862:
436:
411:
245:
3486:
by a very satisfying multiplication of this particular definition as expanded below.
5950:
5933:
5688:(?) function (R→R) transforms addition into multiplication: f(u+v) = f(u) • f(v) .
5284:
2866:
2616:
2378:
5794:
5751:
5647:
5598:
3030:
3751:
2645:
as an object of secondary importance, defined in terms of the important function
5852:
for the defined class of functions. Possibly(?): "the 1 to 1 power functions".
5704:
function (R→R) transforms multiplication into addition: f(uv) = f(u) + f(v) .
2997:
2805:, there is no singularity, and no branching. This is not the case for functions
2656:
2527:
202:
113:
5941:
5926:
5781:
5745:
5606:
5574:
5480:
5430:
5339:
5315:
5292:
5276:
3038:
2986:
2874:
2790:
2763:
2747:
2722:
2624:
2517:
2405:
2386:
2280:
444:
415:
394:
253:
2508:
further down? Is it just that no one has gotten around to implementing this?
90:
2418:
Talk:Exponential function/Archive 1#Confusion in lead about what the topic is
604:{\displaystyle \exp y=\lim _{n\to \infty }\left(1+{\frac {y}{n}}\right)^{n}}
526:{\displaystyle \exp x=\lim _{n\to \infty }\left(1+{\frac {x}{n}}\right)^{n}}
262:
241:
5672:(?) function transforms addition into addition: f(u+v) = f(u) + f(v) .
3611:
268:
2420:), there was an RfC where the consensus was that the primary subject of
2885:
In my opinion, there is an implication that all functions of the form
2339:
shows that this function is equal to its derivative, and equals 1 for
3594:{\displaystyle f\equiv e=B\;\to \;e^{x}\equiv \sum _{j=0}^{\infty }.}
2283:
Wondering if one could improve on that for the edit to be approved
5588:
5581:
exponential functions, exponentiation, exponents, power functions?
2738:
Examples are "e^x", cosine and sine, selection of Taylor series.--
5283:
These huge formulas are certainly not convenient for beginners.
5788:
Dieudonné on defining standard functions by their main property
5359:. Also that it then has to be proved that a non-zero function
205:
169:
15:
5593:
examples of 10 curves with real exponents between -1 and 1.25
2451:. Given this, shouldn't the article begin with and focus on
5932:
Dieudonné's quotation is not a definition. It is a theorem.
5586:
if you'd like help with this... Otherwise, i'll keep quiet.
2801:
near their singularities. As the exponential function is an
2478:(as it did up to 2015) and define the more general variants
5150:
4983:
4019:
2797:
I believe that that you call "branching" is the study of
5889:-4. On p.82 (4.3.2), D. uses as well the main property
2992:
Wiki
Education assignment: 4A Knowledge (XXG) Assignment
5496:, so I think it is right for this article to focus on
3479:{\displaystyle f\times f=f\;\Leftrightarrow \;f=B^{x}}
3379:{\displaystyle g\times g=g\;\Leftrightarrow \;g=B^{x}}
5977:
5450:
3609:
3495:
3395:
3295:
3136:
3055:
2921:
2891:
2861:
is not real and positive. This case is considered in
2811:
2548:
2484:
2457:
2430:
2352:
2297:
620:
539:
461:
355:
326:
285:
2865:, as said in the hatnote at the top of the article.
112:, a collaborative effort to improve the coverage of
2732:A function is exponential when it shows behaviour:
431:I have documented this in this article and also in
5463:
5247:
3593:
3478:
3378:
3279:
3119:
2969:
2907:
2849:
2673:that equals its own derivative and that has value
2579:
2500:
2470:
2443:
2365:
2331:
2261:
603:
525:
373:
341:
312:
3120:{\displaystyle e^{x}\equiv \sum _{j=0}^{\infty }}
2033:
2020:
1961:
1948:
1716:
1703:
1614:
1601:
1399:
1386:
1297:
1284:
1110:
1097:
3386:are equivalent where B is an appropriate base.
2634:common terminology? I am not sure, even though
2177:
1895:
1835:
1578:
1518:
1217:
1058:
965:
869:
766:
706:
654:
553:
475:
2523:I suggest to boldly change the beginning into
5967:Knowledge (XXG) vital articles in Mathematics
5810:"Any continuous mapping R into R such that
213:This page has archives. Sections older than
8:
2412:The primary meaning of exponential function
5258:
2776:
235:
58:
5455:
5449:
5208:
5202:
5185:
5179:
5168:
5111:
5092:
5062:
5043:
5001:
4862:
4856:
4761:
4754:
4738:
4732:
4654:
4638:
4631:
4600:
4593:
4577:
4571:
4501:
4485:
4478:
4450:
4440:
4433:
4402:
4395:
4379:
4373:
4311:
4295:
4288:
4260:
4250:
4222:
4212:
4185:
4156:
4150:
4130:
4124:
4104:
4098:
4078:
4072:
4052:
4037:
3985:
3979:
3964:
3958:
3926:
3920:
3889:
3883:
3868:
3862:
3808:
3802:
3787:
3781:
3750:
3723:
3717:
3712:
3706:
3695:
3676:
3670:
3665:
3659:
3648:
3610:
3608:
3574:
3568:
3555:
3544:
3531:
3494:
3470:
3394:
3370:
3294:
3254:
3242:
3231:
3186:
3180:
3167:
3156:
3135:
3103:
3097:
3084:
3073:
3060:
3054:
2920:
2899:
2890:
2829:
2816:
2810:
2568:
2547:
2492:
2483:
2462:
2456:
2435:
2429:
2357:
2351:
2323:
2314:
2302:
2296:
2206:
2192:
2180:
2171:
2104:
2090:
2074:
2051:
2032:
2019:
2017:
2002:
1979:
1960:
1947:
1945:
1928:
1914:
1898:
1885:
1862:
1838:
1800:
1788:
1774:
1757:
1734:
1715:
1702:
1700:
1685:
1671:
1655:
1632:
1613:
1600:
1598:
1581:
1568:
1545:
1521:
1483:
1471:
1457:
1440:
1417:
1398:
1385:
1383:
1368:
1354:
1338:
1315:
1296:
1283:
1281:
1272:
1249:
1220:
1200:
1194:
1182:
1168:
1151:
1128:
1109:
1096:
1094:
1088:
1077:
1061:
1040:
1027:
1013:
992:
968:
947:
927:
901:
872:
846:
831:
813:
798:
769:
748:
733:
709:
696:
681:
657:
621:
619:
595:
580:
556:
538:
517:
502:
478:
460:
354:
325:
284:
5913:) to charcterize the mapping named the
3525:
3520:
3449:
3444:
3349:
3344:
3210:
3208:
3206:
3204:
3202:
3200:
223:when more than 10 sections are present.
126:Knowledge (XXG):WikiProject Mathematics
60:
19:
5962:Knowledge (XXG) level-4 vital articles
5982:C-Class vital articles in Mathematics
7:
106:This article is within the scope of
5799:A much more recent source (compare
2641:Perhaps it makes sense to think of
49:It is of interest to the following
5525:and thus solves requirements like
5180:
3707:
3660:
3556:
3243:
3168:
3085:
3006:
3002:
2187:
2024:
1952:
1905:
1845:
1707:
1605:
1588:
1528:
1390:
1288:
1227:
1101:
1068:
975:
879:
776:
716:
664:
563:
485:
455:For example, using the definition
14:
5992:Top-priority mathematics articles
5858:-3. D. doesn't mention that the
2850:{\displaystyle a^{x}=e^{x\ln a},}
217:may be automatically archived by
5772:Exponentiation § Power functions
5401:will necessarily be of the form
5344:My changes were to clarify that
3009:. Further details are available
2996:
422:
174:
129:Template:WikiProject Mathematics
93:
83:
62:
29:
20:
2970:{\displaystyle f(x+y)=f(x)f(y)}
2613:Principle of least astonishment
146:This article has been rated as
5972:C-Class level-4 vital articles
5942:17:20, 22 September 2024 (UTC)
5927:16:34, 22 September 2024 (UTC)
5805:Foundations of Modern Analysis
5444:exp and exponential functions
5238:
5226:
5199:
5186:
5108:
5095:
5059:
5046:
5029:
5017:
4790:
4778:
4674:
4662:
4521:
4509:
4331:
4319:
4002:
3939:
3906:
3843:
3825:
3762:
3638:
3632:
3623:
3617:
3585:
3561:
3522:
3505:
3499:
3460:
3454:
3446:
3441:
3429:
3420:
3414:
3405:
3399:
3360:
3354:
3346:
3341:
3329:
3320:
3314:
3305:
3299:
3265:
3248:
3221:
3215:
3197:
3173:
3146:
3140:
3114:
3090:
2964:
2958:
2952:
2946:
2937:
2925:
2748:12:58, 29 September 2021 (UTC)
2558:
2552:
2252:
2240:
2220:
2184:
2162:
2150:
1902:
1842:
1585:
1525:
1224:
1065:
972:
876:
773:
713:
661:
560:
482:
304:
292:
1:
5486:Knowledge (XXG)'s article on
3029:— Assignment last updated by
2875:10:11, 22 February 2022 (UTC)
2791:01:05, 22 February 2022 (UTC)
2723:16:38, 21 February 2021 (UTC)
2625:09:41, 21 February 2021 (UTC)
2518:06:02, 21 February 2021 (UTC)
2332:{\displaystyle e^{x+y}/e^{y}}
120:and see a list of open tasks.
5987:C-Class mathematics articles
5442:natural exponential function
2987:20:32, 6 November 2022 (UTC)
2764:20:50, 6 November 2022 (UTC)
2632:natural exponential function
2536:natural exponential function
5782:23:18, 25 August 2024 (UTC)
5746:18:36, 20 August 2024 (UTC)
5607:01:19, 20 August 2024 (UTC)
5490:discusses expressions like
2580:{\displaystyle f(x)=e^{x},}
269:MOS:MATH#Multi-letter names
6008:
5862:of a given power function
3049:In the formal definition:
313:{\displaystyle \exp(x+y),}
5848:-1. D. doesn't mention a
5575:17:07, 27 June 2024 (UTC)
5481:11:27, 27 June 2024 (UTC)
5431:16:52, 27 June 2024 (UTC)
5340:19:48, 26 June 2024 (UTC)
5316:18:32, 26 June 2024 (UTC)
5293:17:20, 26 June 2024 (UTC)
5277:16:58, 26 June 2024 (UTC)
2881:Inconsistency in the lead
267:For the most part, yes.
145:
78:
57:
5866:is equal to the, not on
3039:00:57, 31 May 2024 (UTC)
2661:the exponential function
2532:the exponential function
2406:17:05, 21 May 2020 (UTC)
2387:16:55, 21 May 2020 (UTC)
2281:16:21, 21 May 2020 (UTC)
445:19:47, 21 May 2020 (UTC)
416:12:56, 21 May 2020 (UTC)
395:19:41, 2 July 2019 (UTC)
374:{\displaystyle \exp ix.}
254:17:57, 2 July 2019 (UTC)
152:project's priority scale
5807:, 1960; p.83 (4.3.7) :
2735:f(a + b) = f(a) * f(b)
2708:an exponential function
2630:Yes, that is good. Is
2604:an exponential function
2424:should be the function
401:Extinction coefficient?
349:or even something like
342:{\displaystyle \exp x,}
109:WikiProject Mathematics
5957:C-Class vital articles
5594:
5465:
5249:
5184:
3711:
3664:
3595:
3560:
3480:
3380:
3281:
3247:
3172:
3121:
3089:
2971:
2909:
2908:{\displaystyle ab^{x}}
2851:
2581:
2534:(sometimes called the
2502:
2501:{\displaystyle ab^{x}}
2472:
2445:
2367:
2333:
2263:
1093:
605:
527:
375:
343:
314:
220:Lowercase sigmabot III
5592:
5466:
5464:{\displaystyle b^{x}}
5250:
5164:
3691:
3644:
3596:
3540:
3481:
3381:
3282:
3227:
3152:
3122:
3069:
3013:. Student editor(s):
2972:
2915:satisfy the identity
2910:
2852:
2799:multivalued functions
2728:Exponential behaviour
2700:, is the base of the
2582:
2503:
2473:
2471:{\displaystyle e^{x}}
2446:
2444:{\displaystyle e^{x}}
2368:
2366:{\displaystyle e^{x}}
2334:
2264:
1073:
606:
528:
376:
344:
315:
43:on Knowledge (XXG)'s
36:level-4 vital article
5762:(which also defines
5756:Exponential function
5448:
3607:
3493:
3393:
3293:
3134:
3053:
2919:
2889:
2809:
2596:is the basis of the
2546:
2482:
2455:
2428:
2422:Exponential function
2350:
2295:
618:
537:
459:
353:
324:
283:
132:mathematics articles
5915:logarithm of base a
5870:dependent, value
3389:Then show and use:
3021:). Peer reviewers:
5834:) has the form
5595:
5461:
5245:
5243:
5148:
4981:
4017:
3591:
3526:
3521:
3476:
3450:
3445:
3376:
3350:
3345:
3277:
3211:
3209:
3207:
3205:
3203:
3201:
3117:
3011:on the course page
2967:
2905:
2847:
2577:
2498:
2468:
2441:
2363:
2346:; thus, it equals
2329:
2259:
2257:
2191:
1909:
1849:
1592:
1532:
1231:
1202:(Binomial theorem)
1072:
979:
883:
780:
720:
668:
601:
567:
523:
489:
371:
339:
310:
101:Mathematics portal
45:content assessment
5279:
5263:comment added by
5126:
5077:
4803:
4687:
4624:
4534:
4471:
4426:
4344:
4281:
4243:
3045:Formal Definition
3023:Maaatttthhheeewww
2793:
2781:comment added by
2702:natural logarithm
2636:natural logarithm
2598:natural logarithm
2212:
2176:
2174:
2110:
2067:
2031:
1995:
1959:
1934:
1894:
1878:
1834:
1794:
1750:
1714:
1691:
1648:
1612:
1577:
1561:
1517:
1477:
1433:
1397:
1374:
1331:
1295:
1265:
1216:
1203:
1188:
1144:
1108:
1057:
1033:
1008:
964:
935:
909:
868:
839:
806:
765:
741:
705:
689:
653:
588:
552:
510:
474:
433:Exponential decay
256:
240:comment added by
227:
226:
166:
165:
162:
161:
158:
157:
5999:
5798:
5709:general power(?)
5693:anti-exponential
5686:anti-logarithmic
5651:
5562:
5555:
5524:
5518:
5511:
5502:
5495:
5470:
5468:
5467:
5462:
5460:
5459:
5418:
5411:
5407:
5400:
5369:
5358:
5350:
5303:
5254:
5252:
5251:
5246:
5244:
5219:
5212:
5207:
5206:
5183:
5178:
5152:
5149:
5127:
5125:
5117:
5116:
5115:
5093:
5078:
5076:
5068:
5067:
5066:
5044:
4985:
4982:
4866:
4861:
4860:
4804:
4802:
4776:
4772:
4771:
4755:
4742:
4737:
4736:
4688:
4686:
4660:
4659:
4658:
4649:
4648:
4632:
4625:
4623:
4609:
4605:
4604:
4594:
4581:
4576:
4575:
4535:
4533:
4507:
4506:
4505:
4496:
4495:
4479:
4472:
4470:
4456:
4455:
4454:
4445:
4444:
4434:
4427:
4425:
4411:
4407:
4406:
4396:
4383:
4378:
4377:
4345:
4343:
4317:
4316:
4315:
4306:
4305:
4289:
4282:
4280:
4266:
4265:
4264:
4251:
4244:
4242:
4228:
4227:
4226:
4213:
4189:
4160:
4155:
4154:
4134:
4129:
4128:
4108:
4103:
4102:
4082:
4077:
4076:
4056:
4021:
4018:
3989:
3984:
3983:
3968:
3963:
3962:
3930:
3925:
3924:
3893:
3888:
3887:
3872:
3867:
3866:
3812:
3807:
3806:
3791:
3786:
3785:
3734:
3727:
3722:
3721:
3710:
3705:
3687:
3680:
3675:
3674:
3663:
3658:
3600:
3598:
3597:
3592:
3578:
3573:
3572:
3559:
3554:
3536:
3535:
3485:
3483:
3482:
3477:
3475:
3474:
3385:
3383:
3382:
3377:
3375:
3374:
3286:
3284:
3283:
3278:
3258:
3246:
3241:
3190:
3185:
3184:
3171:
3166:
3126:
3124:
3123:
3118:
3107:
3102:
3101:
3088:
3083:
3065:
3064:
3041:
3019:article contribs
3008:
3004:
3003:12 February 2024
3000:
2976:
2974:
2973:
2968:
2914:
2912:
2911:
2906:
2904:
2903:
2860:
2856:
2854:
2853:
2848:
2843:
2842:
2821:
2820:
2706:More generally,
2698:
2690:
2684:. Its value at
2683:
2676:
2668:
2650:
2644:
2638:certainly is.
2602:More generally,
2594:
2586:
2584:
2583:
2578:
2573:
2572:
2507:
2505:
2504:
2499:
2497:
2496:
2477:
2475:
2474:
2469:
2467:
2466:
2450:
2448:
2447:
2442:
2440:
2439:
2376:
2372:
2370:
2369:
2364:
2362:
2361:
2345:
2338:
2336:
2335:
2330:
2328:
2327:
2318:
2313:
2312:
2290:
2268:
2266:
2265:
2260:
2258:
2213:
2211:
2210:
2201:
2193:
2190:
2175:
2172:
2132:
2128:
2115:
2111:
2109:
2108:
2099:
2091:
2085:
2084:
2073:
2069:
2068:
2063:
2052:
2038:
2037:
2036:
2023:
2013:
2012:
2001:
1997:
1996:
1991:
1980:
1966:
1965:
1964:
1951:
1939:
1935:
1933:
1932:
1923:
1915:
1908:
1890:
1889:
1884:
1880:
1879:
1874:
1863:
1848:
1822:
1818:
1805:
1804:
1799:
1795:
1793:
1792:
1783:
1775:
1768:
1767:
1756:
1752:
1751:
1746:
1735:
1721:
1720:
1719:
1706:
1696:
1692:
1690:
1689:
1680:
1672:
1666:
1665:
1654:
1650:
1649:
1644:
1633:
1619:
1618:
1617:
1604:
1591:
1573:
1572:
1567:
1563:
1562:
1557:
1546:
1531:
1505:
1501:
1488:
1487:
1482:
1478:
1476:
1475:
1466:
1458:
1451:
1450:
1439:
1435:
1434:
1429:
1418:
1404:
1403:
1402:
1389:
1379:
1375:
1373:
1372:
1363:
1355:
1349:
1348:
1337:
1333:
1332:
1327:
1316:
1302:
1301:
1300:
1287:
1277:
1276:
1271:
1267:
1266:
1261:
1250:
1230:
1204:
1201:
1199:
1198:
1193:
1189:
1187:
1186:
1177:
1169:
1162:
1161:
1150:
1146:
1145:
1140:
1129:
1115:
1114:
1113:
1100:
1092:
1087:
1071:
1045:
1044:
1039:
1035:
1034:
1032:
1031:
1022:
1014:
1009:
1004:
993:
978:
952:
951:
946:
942:
941:
937:
936:
928:
915:
911:
910:
902:
882:
856:
852:
851:
850:
845:
841:
840:
832:
818:
817:
812:
808:
807:
799:
779:
753:
752:
747:
743:
742:
734:
719:
701:
700:
695:
691:
690:
682:
667:
610:
608:
607:
602:
600:
599:
594:
590:
589:
581:
566:
532:
530:
529:
524:
522:
521:
516:
512:
511:
503:
488:
430:
426:
425:
380:
378:
377:
372:
348:
346:
345:
340:
319:
317:
316:
311:
278:
274:
266:
222:
206:
178:
170:
134:
133:
130:
127:
124:
103:
98:
97:
87:
80:
79:
74:
66:
59:
42:
33:
32:
25:
24:
16:
6007:
6006:
6002:
6001:
6000:
5998:
5997:
5996:
5947:
5946:
5845:Four remarks:
5792:
5790:
5734:Cours d'analyse
5645:
5583:
5558:
5526:
5520:
5513:
5505:
5497:
5491:
5451:
5446:
5445:
5414:
5409:
5402:
5371:
5360:
5352:
5345:
5299:
5242:
5241:
5198:
5158:
5157:
5154:
5153:
5147:
5146:
5138:
5136:
5134:
5132:
5129:
5128:
5118:
5107:
5094:
5087:
5085:
5083:
5080:
5079:
5069:
5058:
5045:
5038:
5036:
5033:
5032:
5012:
5009:
5008:
4997:
4991:
4990:
4987:
4986:
4980:
4979:
4971:
4963:
4955:
4947:
4939:
4931:
4922:
4921:
4913:
4905:
4897:
4889:
4881:
4873:
4852:
4846:
4845:
4837:
4829:
4821:
4813:
4805:
4777:
4757:
4756:
4749:
4728:
4722:
4721:
4713:
4705:
4697:
4689:
4661:
4650:
4634:
4633:
4626:
4610:
4596:
4595:
4588:
4567:
4561:
4560:
4552:
4544:
4536:
4508:
4497:
4481:
4480:
4473:
4457:
4446:
4436:
4435:
4428:
4412:
4398:
4397:
4390:
4369:
4363:
4362:
4354:
4346:
4318:
4307:
4291:
4290:
4283:
4267:
4256:
4252:
4245:
4229:
4218:
4214:
4207:
4196:
4176:
4175:
4167:
4146:
4141:
4120:
4115:
4094:
4089:
4068:
4063:
4044:
4033:
4027:
4026:
4023:
4022:
4016:
4015:
4006:
4005:
3975:
3954:
3934:
3916:
3910:
3909:
3879:
3858:
3838:
3829:
3828:
3798:
3777:
3757:
3746:
3740:
3739:
3736:
3735:
3713:
3666:
3605:
3604:
3564:
3527:
3491:
3490:
3466:
3391:
3390:
3366:
3291:
3290:
3176:
3132:
3131:
3093:
3056:
3051:
3050:
3047:
3028:
2994:
2917:
2916:
2895:
2887:
2886:
2883:
2858:
2825:
2812:
2807:
2806:
2803:entire function
2772:
2730:
2693:
2685:
2678:
2674:
2664:
2646:
2642:
2589:
2564:
2544:
2543:
2488:
2480:
2479:
2458:
2453:
2452:
2431:
2426:
2425:
2414:
2374:
2353:
2348:
2347:
2340:
2319:
2298:
2293:
2292:
2288:
2256:
2255:
2227:
2224:
2223:
2202:
2194:
2137:
2134:
2133:
2100:
2092:
2086:
2053:
2044:
2040:
2039:
2018:
1981:
1972:
1968:
1967:
1946:
1944:
1940:
1924:
1916:
1910:
1864:
1855:
1851:
1850:
1827:
1824:
1823:
1784:
1776:
1770:
1769:
1736:
1727:
1723:
1722:
1701:
1681:
1673:
1667:
1634:
1625:
1621:
1620:
1599:
1597:
1593:
1547:
1538:
1534:
1533:
1510:
1507:
1506:
1467:
1459:
1453:
1452:
1419:
1410:
1406:
1405:
1384:
1364:
1356:
1350:
1317:
1308:
1304:
1303:
1282:
1251:
1242:
1238:
1237:
1236:
1232:
1209:
1206:
1205:
1178:
1170:
1164:
1163:
1130:
1121:
1117:
1116:
1095:
1050:
1047:
1046:
1023:
1015:
994:
985:
981:
980:
957:
954:
953:
920:
916:
894:
890:
889:
885:
884:
861:
858:
857:
824:
820:
819:
791:
787:
786:
785:
781:
758:
755:
754:
726:
722:
721:
674:
670:
669:
646:
616:
615:
573:
569:
568:
535:
534:
495:
491:
490:
457:
456:
453:
423:
421:
403:
351:
350:
322:
321:
281:
280:
276:
272:
260:
232:
218:
207:
201:
183:
131:
128:
125:
122:
121:
99:
92:
72:
40:
30:
12:
11:
5:
6005:
6003:
5995:
5994:
5989:
5984:
5979:
5974:
5969:
5964:
5959:
5949:
5948:
5945:
5944:
5789:
5786:
5785:
5784:
5768:Power function
5760:Exponentiation
5748:
5728:
5727:
5722:
5721:
5714:
5713:
5712:
5698:
5697:
5696:
5682:
5681:
5680:
5666:
5665:
5664:
5654:
5653:
5641:
5638:
5635:
5632:
5629:
5626:
5623:
5620:
5617:
5614:
5611:
5582:
5579:
5578:
5577:
5488:exponentiation
5458:
5454:
5438:
5437:
5436:
5435:
5434:
5433:
5328:
5324:
5321:
5295:
5256:
5255:
5240:
5237:
5234:
5231:
5228:
5225:
5222:
5218:
5215:
5211:
5205:
5201:
5197:
5194:
5191:
5188:
5182:
5177:
5174:
5171:
5167:
5163:
5160:
5159:
5156:
5155:
5151:
5145:
5142:
5139:
5137:
5135:
5133:
5131:
5130:
5124:
5121:
5114:
5110:
5106:
5103:
5100:
5097:
5091:
5088:
5086:
5084:
5082:
5081:
5075:
5072:
5065:
5061:
5057:
5054:
5051:
5048:
5042:
5039:
5037:
5035:
5034:
5031:
5028:
5025:
5022:
5019:
5016:
5013:
5011:
5010:
5007:
5004:
5003:
5000:
4996:
4993:
4992:
4989:
4988:
4984:
4978:
4975:
4972:
4970:
4967:
4964:
4962:
4959:
4956:
4954:
4951:
4948:
4946:
4943:
4940:
4938:
4935:
4932:
4930:
4927:
4924:
4923:
4920:
4917:
4914:
4912:
4909:
4906:
4904:
4901:
4898:
4896:
4893:
4890:
4888:
4885:
4882:
4880:
4877:
4874:
4872:
4869:
4865:
4859:
4855:
4851:
4848:
4847:
4844:
4841:
4838:
4836:
4833:
4830:
4828:
4825:
4822:
4820:
4817:
4814:
4812:
4809:
4806:
4801:
4798:
4795:
4792:
4789:
4786:
4783:
4780:
4775:
4770:
4767:
4764:
4760:
4753:
4750:
4748:
4745:
4741:
4735:
4731:
4727:
4724:
4723:
4720:
4717:
4714:
4712:
4709:
4706:
4704:
4701:
4698:
4696:
4693:
4690:
4685:
4682:
4679:
4676:
4673:
4670:
4667:
4664:
4657:
4653:
4647:
4644:
4641:
4637:
4630:
4627:
4622:
4619:
4616:
4613:
4608:
4603:
4599:
4592:
4589:
4587:
4584:
4580:
4574:
4570:
4566:
4563:
4562:
4559:
4556:
4553:
4551:
4548:
4545:
4543:
4540:
4537:
4532:
4529:
4526:
4523:
4520:
4517:
4514:
4511:
4504:
4500:
4494:
4491:
4488:
4484:
4477:
4474:
4469:
4466:
4463:
4460:
4453:
4449:
4443:
4439:
4432:
4429:
4424:
4421:
4418:
4415:
4410:
4405:
4401:
4394:
4391:
4389:
4386:
4382:
4376:
4372:
4368:
4365:
4364:
4361:
4358:
4355:
4353:
4350:
4347:
4342:
4339:
4336:
4333:
4330:
4327:
4324:
4321:
4314:
4310:
4304:
4301:
4298:
4294:
4287:
4284:
4279:
4276:
4273:
4270:
4263:
4259:
4255:
4249:
4246:
4241:
4238:
4235:
4232:
4225:
4221:
4217:
4211:
4208:
4206:
4203:
4200:
4197:
4195:
4192:
4188:
4184:
4181:
4178:
4177:
4174:
4171:
4168:
4166:
4163:
4159:
4153:
4149:
4145:
4142:
4140:
4137:
4133:
4127:
4123:
4119:
4116:
4114:
4111:
4107:
4101:
4097:
4093:
4090:
4088:
4085:
4081:
4075:
4071:
4067:
4064:
4062:
4059:
4055:
4051:
4048:
4045:
4043:
4040:
4039:
4036:
4032:
4029:
4028:
4025:
4024:
4020:
4014:
4011:
4008:
4007:
4004:
4001:
3998:
3995:
3992:
3988:
3982:
3978:
3974:
3971:
3967:
3961:
3957:
3953:
3950:
3947:
3944:
3941:
3938:
3935:
3933:
3929:
3923:
3919:
3915:
3912:
3911:
3908:
3905:
3902:
3899:
3896:
3892:
3886:
3882:
3878:
3875:
3871:
3865:
3861:
3857:
3854:
3851:
3848:
3845:
3842:
3839:
3837:
3834:
3831:
3830:
3827:
3824:
3821:
3818:
3815:
3811:
3805:
3801:
3797:
3794:
3790:
3784:
3780:
3776:
3773:
3770:
3767:
3764:
3761:
3758:
3756:
3753:
3752:
3749:
3745:
3742:
3741:
3738:
3737:
3733:
3730:
3726:
3720:
3716:
3709:
3704:
3701:
3698:
3694:
3690:
3686:
3683:
3679:
3673:
3669:
3662:
3657:
3654:
3651:
3647:
3643:
3640:
3637:
3634:
3631:
3628:
3625:
3622:
3619:
3616:
3613:
3612:
3590:
3587:
3584:
3581:
3577:
3571:
3567:
3563:
3558:
3553:
3550:
3547:
3543:
3539:
3534:
3530:
3524:
3519:
3516:
3513:
3510:
3507:
3504:
3501:
3498:
3473:
3469:
3465:
3462:
3459:
3456:
3453:
3448:
3443:
3440:
3437:
3434:
3431:
3428:
3425:
3422:
3419:
3416:
3413:
3410:
3407:
3404:
3401:
3398:
3373:
3369:
3365:
3362:
3359:
3356:
3353:
3348:
3343:
3340:
3337:
3334:
3331:
3328:
3325:
3322:
3319:
3316:
3313:
3310:
3307:
3304:
3301:
3298:
3276:
3273:
3270:
3267:
3264:
3261:
3257:
3253:
3250:
3245:
3240:
3237:
3234:
3230:
3226:
3223:
3220:
3217:
3214:
3199:
3196:
3193:
3189:
3183:
3179:
3175:
3170:
3165:
3162:
3159:
3155:
3151:
3148:
3145:
3142:
3139:
3116:
3113:
3110:
3106:
3100:
3096:
3092:
3087:
3082:
3079:
3076:
3072:
3068:
3063:
3059:
3046:
3043:
2993:
2990:
2966:
2963:
2960:
2957:
2954:
2951:
2948:
2945:
2942:
2939:
2936:
2933:
2930:
2927:
2924:
2902:
2898:
2894:
2882:
2879:
2878:
2877:
2863:Exponentiation
2846:
2841:
2838:
2835:
2832:
2828:
2824:
2819:
2815:
2771:
2768:
2767:
2766:
2729:
2726:
2712:
2711:
2705:
2628:
2627:
2609:
2608:
2607:
2601:
2576:
2571:
2567:
2563:
2560:
2557:
2554:
2551:
2542:
2495:
2491:
2487:
2465:
2461:
2438:
2434:
2413:
2410:
2409:
2408:
2389:
2360:
2356:
2326:
2322:
2317:
2311:
2308:
2305:
2301:
2270:
2269:
2254:
2251:
2248:
2245:
2242:
2239:
2236:
2233:
2230:
2228:
2226:
2225:
2222:
2219:
2216:
2209:
2205:
2200:
2197:
2189:
2186:
2183:
2179:
2170:
2167:
2164:
2161:
2158:
2155:
2152:
2149:
2146:
2143:
2140:
2138:
2136:
2135:
2131:
2127:
2124:
2121:
2118:
2114:
2107:
2103:
2098:
2095:
2089:
2083:
2080:
2077:
2072:
2066:
2062:
2059:
2056:
2050:
2047:
2043:
2035:
2030:
2027:
2022:
2016:
2011:
2008:
2005:
2000:
1994:
1990:
1987:
1984:
1978:
1975:
1971:
1963:
1958:
1955:
1950:
1943:
1938:
1931:
1927:
1922:
1919:
1913:
1907:
1904:
1901:
1897:
1893:
1888:
1883:
1877:
1873:
1870:
1867:
1861:
1858:
1854:
1847:
1844:
1841:
1837:
1833:
1830:
1828:
1826:
1825:
1821:
1817:
1814:
1811:
1808:
1803:
1798:
1791:
1787:
1782:
1779:
1773:
1766:
1763:
1760:
1755:
1749:
1745:
1742:
1739:
1733:
1730:
1726:
1718:
1713:
1710:
1705:
1699:
1695:
1688:
1684:
1679:
1676:
1670:
1664:
1661:
1658:
1653:
1647:
1643:
1640:
1637:
1631:
1628:
1624:
1616:
1611:
1608:
1603:
1596:
1590:
1587:
1584:
1580:
1576:
1571:
1566:
1560:
1556:
1553:
1550:
1544:
1541:
1537:
1530:
1527:
1524:
1520:
1516:
1513:
1511:
1509:
1508:
1504:
1500:
1497:
1494:
1491:
1486:
1481:
1474:
1470:
1465:
1462:
1456:
1449:
1446:
1443:
1438:
1432:
1428:
1425:
1422:
1416:
1413:
1409:
1401:
1396:
1393:
1388:
1382:
1378:
1371:
1367:
1362:
1359:
1353:
1347:
1344:
1341:
1336:
1330:
1326:
1323:
1320:
1314:
1311:
1307:
1299:
1294:
1291:
1286:
1280:
1275:
1270:
1264:
1260:
1257:
1254:
1248:
1245:
1241:
1235:
1229:
1226:
1223:
1219:
1215:
1212:
1210:
1208:
1207:
1197:
1192:
1185:
1181:
1176:
1173:
1167:
1160:
1157:
1154:
1149:
1143:
1139:
1136:
1133:
1127:
1124:
1120:
1112:
1107:
1104:
1099:
1091:
1086:
1083:
1080:
1076:
1070:
1067:
1064:
1060:
1056:
1053:
1051:
1049:
1048:
1043:
1038:
1030:
1026:
1021:
1018:
1012:
1007:
1003:
1000:
997:
991:
988:
984:
977:
974:
971:
967:
963:
960:
958:
956:
955:
950:
945:
940:
934:
931:
926:
923:
919:
914:
908:
905:
900:
897:
893:
888:
881:
878:
875:
871:
867:
864:
862:
860:
859:
855:
849:
844:
838:
835:
830:
827:
823:
816:
811:
805:
802:
797:
794:
790:
784:
778:
775:
772:
768:
764:
761:
759:
757:
756:
751:
746:
740:
737:
732:
729:
725:
718:
715:
712:
708:
704:
699:
694:
688:
685:
680:
677:
673:
666:
663:
660:
656:
652:
649:
647:
645:
642:
639:
636:
633:
630:
627:
624:
623:
598:
593:
587:
584:
579:
576:
572:
565:
562:
559:
555:
551:
548:
545:
542:
520:
515:
509:
506:
501:
498:
494:
487:
484:
481:
477:
473:
470:
467:
464:
452:
449:
448:
447:
402:
399:
398:
397:
370:
367:
364:
361:
358:
338:
335:
332:
329:
309:
306:
303:
300:
297:
294:
291:
288:
231:
228:
225:
224:
212:
209:
208:
203:
199:
197:
194:
193:
185:
184:
179:
173:
164:
163:
160:
159:
156:
155:
144:
138:
137:
135:
118:the discussion
105:
104:
88:
76:
75:
67:
55:
54:
48:
26:
13:
10:
9:
6:
4:
3:
2:
6004:
5993:
5990:
5988:
5985:
5983:
5980:
5978:
5975:
5973:
5970:
5968:
5965:
5963:
5960:
5958:
5955:
5954:
5952:
5943:
5939:
5935:
5931:
5930:
5929:
5928:
5924:
5920:
5916:
5912:
5908:
5904:
5900:
5896:
5892:
5887:
5885:
5881:
5877:
5873:
5869:
5865:
5861:
5856:
5853:
5851:
5846:
5843:
5841:
5837:
5833:
5829:
5825:
5821:
5817:
5813:
5808:
5806:
5802:
5796:
5787:
5783:
5780:
5777:
5773:
5770:redirects to
5769:
5765:
5761:
5757:
5753:
5749:
5747:
5743:
5739:
5735:
5730:
5729:
5724:
5723:
5719:
5715:
5710:
5706:
5705:
5703:
5699:
5694:
5690:
5689:
5687:
5683:
5678:
5674:
5673:
5671:
5667:
5662:
5658:
5657:
5656:
5655:
5649:
5644:
5643:
5642:
5639:
5636:
5633:
5630:
5627:
5624:
5621:
5618:
5615:
5612:
5609:
5608:
5604:
5600:
5591:
5587:
5580:
5576:
5572:
5568:
5564:
5561:
5553:
5549:
5545:
5541:
5537:
5533:
5529:
5523:
5517:
5509:
5501:
5494:
5489:
5485:
5484:
5483:
5482:
5478:
5474:
5456:
5452:
5443:
5432:
5428:
5424:
5420:
5417:
5406:
5398:
5394:
5390:
5386:
5382:
5378:
5374:
5367:
5363:
5356:
5349:
5343:
5342:
5341:
5337:
5333:
5329:
5325:
5322:
5319:
5318:
5317:
5313:
5309:
5305:
5302:
5296:
5294:
5290:
5286:
5282:
5281:
5280:
5278:
5274:
5270:
5266:
5262:
5235:
5232:
5229:
5223:
5220:
5216:
5213:
5209:
5203:
5195:
5192:
5189:
5175:
5172:
5169:
5165:
5161:
5143:
5140:
5122:
5119:
5112:
5104:
5101:
5098:
5089:
5073:
5070:
5063:
5055:
5052:
5049:
5040:
5026:
5023:
5020:
5014:
5005:
4998:
4994:
4976:
4973:
4968:
4965:
4960:
4957:
4952:
4949:
4944:
4941:
4936:
4933:
4928:
4925:
4918:
4915:
4910:
4907:
4902:
4899:
4894:
4891:
4886:
4883:
4878:
4875:
4870:
4867:
4863:
4857:
4853:
4849:
4842:
4839:
4834:
4831:
4826:
4823:
4818:
4815:
4810:
4807:
4799:
4796:
4793:
4787:
4784:
4781:
4773:
4768:
4765:
4762:
4758:
4751:
4746:
4743:
4739:
4733:
4729:
4725:
4718:
4715:
4710:
4707:
4702:
4699:
4694:
4691:
4683:
4680:
4677:
4671:
4668:
4665:
4655:
4651:
4645:
4642:
4639:
4635:
4628:
4620:
4617:
4614:
4611:
4606:
4601:
4597:
4590:
4585:
4582:
4578:
4572:
4568:
4564:
4557:
4554:
4549:
4546:
4541:
4538:
4530:
4527:
4524:
4518:
4515:
4512:
4502:
4498:
4492:
4489:
4486:
4482:
4475:
4467:
4464:
4461:
4458:
4451:
4447:
4441:
4437:
4430:
4422:
4419:
4416:
4413:
4408:
4403:
4399:
4392:
4387:
4384:
4380:
4374:
4370:
4366:
4359:
4356:
4351:
4348:
4340:
4337:
4334:
4328:
4325:
4322:
4312:
4308:
4302:
4299:
4296:
4292:
4285:
4277:
4274:
4271:
4268:
4261:
4257:
4253:
4247:
4239:
4236:
4233:
4230:
4223:
4219:
4215:
4209:
4204:
4201:
4198:
4193:
4190:
4186:
4182:
4179:
4172:
4169:
4164:
4161:
4157:
4151:
4147:
4143:
4138:
4135:
4131:
4125:
4121:
4117:
4112:
4109:
4105:
4099:
4095:
4091:
4086:
4083:
4079:
4073:
4069:
4065:
4060:
4057:
4053:
4049:
4046:
4041:
4034:
4030:
4012:
4009:
3999:
3996:
3993:
3990:
3986:
3980:
3976:
3972:
3969:
3965:
3959:
3955:
3951:
3948:
3945:
3942:
3936:
3931:
3927:
3921:
3917:
3913:
3903:
3900:
3897:
3894:
3890:
3884:
3880:
3876:
3873:
3869:
3863:
3859:
3855:
3852:
3849:
3846:
3840:
3835:
3832:
3822:
3819:
3816:
3813:
3809:
3803:
3799:
3795:
3792:
3788:
3782:
3778:
3774:
3771:
3768:
3765:
3759:
3754:
3747:
3743:
3731:
3728:
3724:
3718:
3714:
3702:
3699:
3696:
3692:
3688:
3684:
3681:
3677:
3671:
3667:
3655:
3652:
3649:
3645:
3641:
3635:
3629:
3626:
3620:
3614:
3603:
3602:
3601:
3588:
3582:
3579:
3575:
3569:
3565:
3551:
3548:
3545:
3541:
3537:
3532:
3528:
3517:
3514:
3511:
3508:
3502:
3496:
3487:
3471:
3467:
3463:
3457:
3451:
3438:
3435:
3432:
3426:
3423:
3417:
3411:
3408:
3402:
3396:
3387:
3371:
3367:
3363:
3357:
3351:
3338:
3335:
3332:
3326:
3323:
3317:
3311:
3308:
3302:
3296:
3287:
3274:
3271:
3268:
3262:
3259:
3255:
3251:
3238:
3235:
3232:
3228:
3224:
3218:
3212:
3194:
3191:
3187:
3181:
3177:
3163:
3160:
3157:
3153:
3149:
3143:
3137:
3128:
3111:
3108:
3104:
3098:
3094:
3080:
3077:
3074:
3070:
3066:
3061:
3057:
3044:
3042:
3040:
3036:
3032:
3026:
3024:
3020:
3016:
3012:
2999:
2991:
2989:
2988:
2984:
2980:
2961:
2955:
2949:
2943:
2940:
2934:
2931:
2928:
2922:
2900:
2896:
2892:
2880:
2876:
2872:
2868:
2864:
2844:
2839:
2836:
2833:
2830:
2826:
2822:
2817:
2813:
2804:
2800:
2796:
2795:
2794:
2792:
2788:
2784:
2783:77.61.180.106
2780:
2769:
2765:
2761:
2757:
2752:
2751:
2750:
2749:
2745:
2741:
2740:86.83.108.100
2736:
2733:
2727:
2725:
2724:
2720:
2716:
2715:Ebony Jackson
2709:
2703:
2699:
2696:
2688:
2681:
2672:
2667:
2662:
2658:
2654:
2653:
2652:
2649:
2639:
2637:
2633:
2626:
2622:
2618:
2614:
2610:
2605:
2599:
2595:
2592:
2574:
2569:
2565:
2561:
2555:
2549:
2541:
2537:
2533:
2529:
2525:
2524:
2522:
2521:
2520:
2519:
2515:
2511:
2510:Ebony Jackson
2493:
2489:
2485:
2463:
2459:
2436:
2432:
2423:
2419:
2416:In 2016 (see
2411:
2407:
2403:
2399:
2395:
2394:Deacon Vorbis
2390:
2388:
2384:
2380:
2358:
2354:
2343:
2324:
2320:
2315:
2309:
2306:
2303:
2299:
2286:
2285:
2284:
2282:
2278:
2274:
2249:
2246:
2243:
2237:
2234:
2231:
2229:
2217:
2214:
2207:
2203:
2198:
2195:
2181:
2168:
2165:
2159:
2156:
2153:
2147:
2144:
2141:
2139:
2129:
2125:
2122:
2119:
2116:
2112:
2105:
2101:
2096:
2093:
2087:
2081:
2078:
2075:
2070:
2064:
2060:
2057:
2054:
2048:
2045:
2041:
2028:
2025:
2014:
2009:
2006:
2003:
1998:
1992:
1988:
1985:
1982:
1976:
1973:
1969:
1956:
1953:
1941:
1936:
1929:
1925:
1920:
1917:
1911:
1899:
1891:
1886:
1881:
1875:
1871:
1868:
1865:
1859:
1856:
1852:
1839:
1831:
1829:
1819:
1815:
1812:
1809:
1806:
1801:
1796:
1789:
1785:
1780:
1777:
1771:
1764:
1761:
1758:
1753:
1747:
1743:
1740:
1737:
1731:
1728:
1724:
1711:
1708:
1697:
1693:
1686:
1682:
1677:
1674:
1668:
1662:
1659:
1656:
1651:
1645:
1641:
1638:
1635:
1629:
1626:
1622:
1609:
1606:
1594:
1582:
1574:
1569:
1564:
1558:
1554:
1551:
1548:
1542:
1539:
1535:
1522:
1514:
1512:
1502:
1498:
1495:
1492:
1489:
1484:
1479:
1472:
1468:
1463:
1460:
1454:
1447:
1444:
1441:
1436:
1430:
1426:
1423:
1420:
1414:
1411:
1407:
1394:
1391:
1380:
1376:
1369:
1365:
1360:
1357:
1351:
1345:
1342:
1339:
1334:
1328:
1324:
1321:
1318:
1312:
1309:
1305:
1292:
1289:
1278:
1273:
1268:
1262:
1258:
1255:
1252:
1246:
1243:
1239:
1233:
1221:
1213:
1211:
1195:
1190:
1183:
1179:
1174:
1171:
1165:
1158:
1155:
1152:
1147:
1141:
1137:
1134:
1131:
1125:
1122:
1118:
1105:
1102:
1089:
1084:
1081:
1078:
1074:
1062:
1054:
1052:
1041:
1036:
1028:
1024:
1019:
1016:
1010:
1005:
1001:
998:
995:
989:
986:
982:
969:
961:
959:
948:
943:
938:
932:
929:
924:
921:
917:
912:
906:
903:
898:
895:
891:
886:
873:
865:
863:
853:
847:
842:
836:
833:
828:
825:
821:
814:
809:
803:
800:
795:
792:
788:
782:
770:
762:
760:
749:
744:
738:
735:
730:
727:
723:
710:
702:
697:
692:
686:
683:
678:
675:
671:
658:
650:
648:
643:
640:
637:
634:
631:
628:
625:
614:
613:
612:
596:
591:
585:
582:
577:
574:
570:
557:
549:
546:
543:
540:
518:
513:
507:
504:
499:
496:
492:
479:
471:
468:
465:
462:
450:
446:
442:
438:
434:
429:
420:
419:
418:
417:
413:
409:
400:
396:
392:
388:
384:
383:Deacon Vorbis
368:
365:
362:
359:
356:
336:
333:
330:
327:
307:
301:
298:
295:
289:
286:
270:
264:
259:
258:
257:
255:
251:
247:
243:
239:
229:
221:
216:
211:
210:
196:
195:
192:
191:
187:
186:
182:
177:
172:
171:
168:
153:
149:
143:
140:
139:
136:
119:
115:
111:
110:
102:
96:
91:
89:
86:
82:
81:
77:
71:
68:
65:
61:
56:
52:
46:
38:
37:
27:
23:
18:
17:
5914:
5910:
5906:
5902:
5898:
5894:
5890:
5888:
5883:
5879:
5875:
5871:
5867:
5863:
5859:
5857:
5854:
5849:
5847:
5844:
5839:
5835:
5831:
5827:
5823:
5819:
5815:
5811:
5809:
5804:
5800:
5791:
5763:
5733:
5717:
5708:
5701:
5692:
5685:
5676:
5670:proportional
5669:
5660:
5640:
5637:
5634:
5631:
5628:
5625:
5622:
5619:
5616:
5613:
5610:
5596:
5584:
5559:
5551:
5547:
5543:
5539:
5535:
5531:
5527:
5521:
5515:
5507:
5499:
5492:
5441:
5439:
5415:
5404:
5396:
5392:
5388:
5384:
5380:
5376:
5372:
5365:
5361:
5354:
5347:
5300:
5259:— Preceding
5257:
3488:
3388:
3288:
3129:
3048:
3027:
3007:14 June 2024
2995:
2884:
2777:— Preceding
2773:
2737:
2734:
2731:
2713:
2707:
2697:= 2.71828...
2694:
2686:
2679:
2665:
2660:
2647:
2640:
2635:
2631:
2629:
2603:
2593:= 2.71828...
2590:
2535:
2531:
2415:
2341:
2273:49.147.83.13
2271:
454:
427:
404:
236:— Preceding
233:
214:
188:
180:
167:
148:Top-priority
147:
107:
73:Top‑priority
51:WikiProjects
34:
5766:); for now
5702:logarithmic
5677:exponential
5599:Lee De Cola
5473:Tito Omburo
5370:satisfying
5327:factorials.
2657:mathematics
2528:mathematics
320:but not in
230:Parentheses
123:Mathematics
114:mathematics
70:Mathematics
5951:Categories
5519:acts like
2979:Student298
2756:Student298
2691:, denoted
2663:, denoted
2373:for every
5776:jacobolus
5510:= (exp 1)
5408:for some
5357:= (exp 1)
5332:MikeL2468
5265:MikeL2468
3015:Not Fidel
2669:, is the
2538:) is the
437:Anita5192
39:is rated
5934:D.Lazard
5764:exponent
5571:contribs
5563:uantling
5427:contribs
5419:uantling
5312:contribs
5304:uantling
5285:D.Lazard
5273:contribs
5261:unsigned
2867:D.Lazard
2779:unsigned
2770:Branches
2671:function
2617:D.Lazard
2540:function
2379:D.Lazard
250:contribs
238:unsigned
215:365 days
181:Archives
5919:Hesselp
5842:real."
5795:Ldecola
5752:Ldecola
5738:Hesselp
5661:lineair
5648:Ldecola
3031:Ahlluhn
150:on the
41:C-class
5860:degree
5801:Cauchy
3489:Hence
2710:is ...
2606:is ...
2587:where
2402:videos
2398:carbon
391:videos
387:carbon
47:scale.
5886:) .
5838:with
5718:power
5684:* An
2857:when
28:This
5938:talk
5923:talk
5905:) +
5897:) =
5878:) /
5872:x f'
5850:name
5818:) =
5758:and
5742:talk
5726:etc.
5716:* A
5700:* A
5668:* A
5603:talk
5567:talk
5556:. —
5538:) =
5514:exp
5506:exp
5498:exp
5477:talk
5423:talk
5412:. —
5403:exp
5383:) =
5353:exp
5346:exp
5336:talk
5308:talk
5289:talk
5269:talk
3289:(b)
3130:(a)
3035:talk
3005:and
2983:talk
2871:talk
2787:talk
2760:talk
2744:talk
2719:talk
2621:talk
2514:talk
2383:talk
2277:talk
533:and
441:talk
428:Done
412:talk
408:Ywaz
263:A1E6
246:talk
242:A1E6
5917:.
5779:(t)
5691:An
5675:An
2689:= 1
2682:= 0
2677:at
2659:,
2655:In
2530:,
2526:In
2344:= 0
2291:of
2235:exp
2178:lim
2173:(as
2145:exp
1896:lim
1836:lim
1579:lim
1519:lim
1218:lim
1059:lim
966:lim
870:lim
767:lim
707:lim
655:lim
638:exp
626:exp
554:lim
541:exp
476:lim
463:exp
357:exp
328:exp
287:exp
277:exp
273:sin
142:Top
5953::
5940:)
5925:)
5895:xy
5826:)
5816:xy
5744:)
5707:A
5659:A
5605:)
5597:.
5573:)
5569:|
5534:+
5516:kx
5479:)
5429:)
5425:|
5405:kx
5379:+
5338:)
5314:)
5310:|
5291:)
5275:)
5271:•
5181:∞
5166:∑
5144:…
4977:…
4969:…
4961:…
4953:…
4945:…
4937:…
4929:…
4919:…
4911:…
4903:…
4895:…
4887:…
4879:…
4843:…
4835:…
4827:…
4819:…
4811:…
4785:−
4766:−
4719:…
4711:…
4703:…
4695:…
4669:−
4643:−
4558:…
4550:…
4542:…
4516:−
4490:−
4360:…
4352:…
4326:−
4300:−
4173:…
4013:…
4000:…
3937:×
3904:…
3841:×
3823:…
3760:×
3708:∞
3693:∑
3689:×
3661:∞
3646:∑
3627:×
3557:∞
3542:∑
3538:≡
3523:→
3509:≡
3447:⇔
3409:×
3347:⇔
3309:×
3269:≡
3244:∞
3229:∑
3225:≡
3169:∞
3154:∑
3150:≡
3086:∞
3071:∑
3067:≡
3037:)
3025:.
2985:)
2873:)
2837:
2834:ln
2789:)
2762:)
2746:)
2721:)
2623:)
2516:)
2404:)
2400:•
2385:)
2279:)
2238:
2188:∞
2185:→
2148:
2079:−
2007:−
1906:∞
1903:→
1846:∞
1843:→
1762:−
1660:−
1589:∞
1586:→
1529:∞
1526:→
1445:−
1343:−
1228:∞
1225:→
1156:−
1075:∑
1069:∞
1066:→
976:∞
973:→
880:∞
877:→
777:∞
774:→
717:∞
714:→
703:⋅
665:∞
662:→
641:
635:⋅
629:
611:,
564:∞
561:→
544:
486:∞
483:→
466:
443:)
435:.—
414:)
393:)
389:•
360:
331:
290:
275:,
252:)
248:•
5936:(
5921:(
5911:y
5909:(
5907:f
5903:x
5901:(
5899:f
5893:(
5891:f
5884:x
5882:(
5880:f
5876:x
5874:(
5868:x
5864:f
5840:a
5836:x
5832:y
5830:(
5828:g
5824:x
5822:(
5820:g
5814:(
5812:g
5797::
5793:@
5750:@
5740:(
5650::
5646:@
5601:(
5565:(
5560:Q
5554:)
5552:y
5550:(
5548:f
5546:)
5544:x
5542:(
5540:f
5536:y
5532:x
5530:(
5528:f
5522:b
5508:x
5500:x
5493:b
5475:(
5457:x
5453:b
5421:(
5416:Q
5410:k
5399:)
5397:y
5395:(
5393:f
5391:)
5389:x
5387:(
5385:f
5381:y
5377:x
5375:(
5373:f
5368:)
5366:x
5364:(
5362:f
5355:x
5348:x
5334:(
5306:(
5301:Q
5287:(
5267:(
5239:]
5236:y
5233:+
5230:x
5227:[
5224:f
5221:=
5217:!
5214:n
5210:/
5204:n
5200:)
5196:y
5193:+
5190:x
5187:(
5176:0
5173:=
5170:n
5162:=
5141:+
5123:!
5120:n
5113:n
5109:)
5105:y
5102:+
5099:x
5096:(
5090:+
5074:!
5071:2
5064:2
5060:)
5056:y
5053:+
5050:x
5047:(
5041:+
5030:)
5027:y
5024:+
5021:x
5018:(
5015:+
5006:1
4999:{
4995:=
4974:+
4966:+
4958:+
4950:+
4942:+
4934:+
4926:+
4916:+
4908:+
4900:+
4892:+
4884:+
4876:+
4871:!
4868:n
4864:/
4858:n
4854:x
4850:+
4840:+
4832:+
4824:+
4816:+
4808:+
4800:!
4797:1
4794:!
4791:)
4788:1
4782:n
4779:(
4774:y
4769:1
4763:n
4759:x
4752:+
4747:!
4744:4
4740:/
4734:4
4730:x
4726:+
4716:+
4708:+
4700:+
4692:+
4684:!
4681:2
4678:!
4675:)
4672:2
4666:n
4663:(
4656:2
4652:y
4646:2
4640:n
4636:x
4629:+
4621:!
4618:1
4615:!
4612:3
4607:y
4602:3
4598:x
4591:+
4586:!
4583:3
4579:/
4573:3
4569:x
4565:+
4555:+
4547:+
4539:+
4531:!
4528:3
4525:!
4522:)
4519:3
4513:n
4510:(
4503:3
4499:y
4493:3
4487:n
4483:x
4476:+
4468:!
4465:2
4462:!
4459:2
4452:2
4448:y
4442:2
4438:x
4431:+
4423:!
4420:1
4417:!
4414:2
4409:y
4404:2
4400:x
4393:+
4388:!
4385:2
4381:/
4375:2
4371:x
4367:+
4357:+
4349:+
4341:!
4338:4
4335:!
4332:)
4329:4
4323:n
4320:(
4313:4
4309:y
4303:4
4297:n
4293:x
4286:+
4278:!
4275:3
4272:!
4269:1
4262:3
4258:y
4254:x
4248:+
4240:!
4237:2
4234:!
4231:1
4224:2
4220:y
4216:x
4210:+
4205:y
4202:x
4199:+
4194:!
4191:1
4187:/
4183:x
4180:+
4170:+
4165:!
4162:n
4158:/
4152:n
4148:y
4144:+
4139:!
4136:4
4132:/
4126:4
4122:y
4118:+
4113:!
4110:3
4106:/
4100:3
4096:y
4092:+
4087:!
4084:2
4080:/
4074:2
4070:y
4066:+
4061:!
4058:1
4054:/
4050:y
4047:+
4042:1
4035:{
4031:=
4010:+
4003:)
3997:+
3994:!
3991:3
3987:/
3981:3
3977:y
3973:+
3970:2
3966:/
3960:2
3956:y
3952:+
3949:y
3946:+
3943:1
3940:(
3932:2
3928:/
3922:2
3918:x
3914:+
3907:)
3901:+
3898:!
3895:3
3891:/
3885:3
3881:y
3877:+
3874:2
3870:/
3864:2
3860:y
3856:+
3853:y
3850:+
3847:1
3844:(
3836:x
3833:+
3826:)
3820:+
3817:!
3814:3
3810:/
3804:3
3800:y
3796:+
3793:2
3789:/
3783:2
3779:y
3775:+
3772:y
3769:+
3766:1
3763:(
3755:1
3748:{
3744:=
3732:!
3729:k
3725:/
3719:k
3715:y
3703:0
3700:=
3697:k
3685:!
3682:j
3678:/
3672:j
3668:x
3656:0
3653:=
3650:j
3642:=
3639:]
3636:y
3633:[
3630:f
3624:]
3621:x
3618:[
3615:f
3589:.
3586:]
3583:!
3580:j
3576:/
3570:j
3566:x
3562:[
3552:0
3549:=
3546:j
3533:x
3529:e
3518:B
3515:=
3512:e
3506:]
3503:1
3500:[
3497:f
3472:x
3468:B
3464:=
3461:]
3458:x
3455:[
3452:f
3442:]
3439:y
3436:+
3433:x
3430:[
3427:f
3424:=
3421:]
3418:y
3415:[
3412:f
3406:]
3403:x
3400:[
3397:f
3372:x
3368:B
3364:=
3361:]
3358:x
3355:[
3352:g
3342:]
3339:y
3336:+
3333:x
3330:[
3327:g
3324:=
3321:]
3318:y
3315:[
3312:g
3306:]
3303:x
3300:[
3297:g
3275:.
3272:e
3266:]
3263:!
3260:j
3256:/
3252:1
3249:[
3239:0
3236:=
3233:j
3222:]
3219:1
3216:[
3213:f
3198:]
3195:!
3192:j
3188:/
3182:j
3178:x
3174:[
3164:0
3161:=
3158:j
3147:]
3144:x
3141:[
3138:f
3115:]
3112:!
3109:j
3105:/
3099:j
3095:x
3091:[
3081:0
3078:=
3075:j
3062:x
3058:e
3033:(
3017:(
2981:(
2965:)
2962:y
2959:(
2956:f
2953:)
2950:x
2947:(
2944:f
2941:=
2938:)
2935:y
2932:+
2929:x
2926:(
2923:f
2901:x
2897:b
2893:a
2869:(
2859:a
2845:,
2840:a
2831:x
2827:e
2823:=
2818:x
2814:a
2785:(
2758:(
2742:(
2717:(
2704:.
2695:e
2687:x
2680:x
2675:1
2666:e
2648:e
2643:e
2619:(
2600:.
2591:e
2575:,
2570:x
2566:e
2562:=
2559:)
2556:x
2553:(
2550:f
2512:(
2494:x
2490:b
2486:a
2464:x
2460:e
2437:x
2433:e
2396:(
2392:–
2381:(
2375:x
2359:x
2355:e
2342:x
2325:y
2321:e
2316:/
2310:y
2307:+
2304:x
2300:e
2289:x
2275:(
2253:)
2250:y
2247:+
2244:x
2241:(
2232:=
2221:)
2218:0
2215:=
2208:2
2204:n
2199:y
2196:x
2182:n
2169:0
2166:+
2163:)
2160:y
2157:+
2154:x
2151:(
2142:=
2130:]
2126:.
2123:.
2120:.
2117:+
2113:)
2106:2
2102:n
2097:y
2094:x
2088:(
2082:2
2076:n
2071:)
2065:n
2061:y
2058:+
2055:x
2049:+
2046:1
2042:(
2034:)
2029:2
2026:n
2021:(
2015:+
2010:1
2004:n
1999:)
1993:n
1989:y
1986:+
1983:x
1977:+
1974:1
1970:(
1962:)
1957:1
1954:n
1949:(
1942:[
1937:)
1930:2
1926:n
1921:y
1918:x
1912:(
1900:n
1892:+
1887:n
1882:)
1876:n
1872:y
1869:+
1866:x
1860:+
1857:1
1853:(
1840:n
1832:=
1820:]
1816:.
1813:.
1810:.
1807:+
1802:2
1797:)
1790:2
1786:n
1781:y
1778:x
1772:(
1765:2
1759:n
1754:)
1748:n
1744:y
1741:+
1738:x
1732:+
1729:1
1725:(
1717:)
1712:2
1709:n
1704:(
1698:+
1694:)
1687:2
1683:n
1678:y
1675:x
1669:(
1663:1
1657:n
1652:)
1646:n
1642:y
1639:+
1636:x
1630:+
1627:1
1623:(
1615:)
1610:1
1607:n
1602:(
1595:[
1583:n
1575:+
1570:n
1565:)
1559:n
1555:y
1552:+
1549:x
1543:+
1540:1
1536:(
1523:n
1515:=
1503:]
1499:.
1496:.
1493:.
1490:+
1485:2
1480:)
1473:2
1469:n
1464:y
1461:x
1455:(
1448:2
1442:n
1437:)
1431:n
1427:y
1424:+
1421:x
1415:+
1412:1
1408:(
1400:)
1395:2
1392:n
1387:(
1381:+
1377:)
1370:2
1366:n
1361:y
1358:x
1352:(
1346:1
1340:n
1335:)
1329:n
1325:y
1322:+
1319:x
1313:+
1310:1
1306:(
1298:)
1293:1
1290:n
1285:(
1279:+
1274:n
1269:)
1263:n
1259:y
1256:+
1253:x
1247:+
1244:1
1240:(
1234:[
1222:n
1214:=
1196:k
1191:)
1184:2
1180:n
1175:y
1172:x
1166:(
1159:k
1153:n
1148:)
1142:n
1138:y
1135:+
1132:x
1126:+
1123:1
1119:(
1111:)
1106:k
1103:n
1098:(
1090:n
1085:0
1082:=
1079:k
1063:n
1055:=
1042:n
1037:)
1029:2
1025:n
1020:y
1017:x
1011:+
1006:n
1002:y
999:+
996:x
990:+
987:1
983:(
970:n
962:=
949:n
944:]
939:)
933:n
930:y
925:+
922:1
918:(
913:)
907:n
904:x
899:+
896:1
892:(
887:[
874:n
866:=
854:]
848:n
843:)
837:n
834:y
829:+
826:1
822:(
815:n
810:)
804:n
801:x
796:+
793:1
789:(
783:[
771:n
763:=
750:n
745:)
739:n
736:y
731:+
728:1
724:(
711:n
698:n
693:)
687:n
684:x
679:+
676:1
672:(
659:n
651:=
644:y
632:x
597:n
592:)
586:n
583:y
578:+
575:1
571:(
558:n
550:=
547:y
519:n
514:)
508:n
505:x
500:+
497:1
493:(
480:n
472:=
469:x
439:(
410:(
385:(
381:–
369:.
366:x
363:i
337:,
334:x
308:,
305:)
302:y
299:+
296:x
293:(
265::
261:@
244:(
190:1
154:.
53::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
