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File:Chebyshev.svg

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set term svg set out 'chebyshev.svg' set data style lines unset zeroaxis set xtics border set ytics border set bmargin 5 set lmargin 7 set title "Chebyshev (summatory von Mangoldt) function" set xlabel "n" 1,0 set ylabel "psi(n)-n+log(pi)" 1, 0 plot "chebyshev.dat" using 1:2 title "" with lines
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for values of ''n'' from 1 to 10,000. Note the remarkably chaotic, unpredictable movement of this function. == Licensing == Created by
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This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
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The following pages on the English Knowledge (XXG) use this file (pages on other projects are not listed):
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If you think that a local copy of this file should be retained, then replace this Template with
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Permission is granted to copy, distribute and/or modify this document under the terms of the
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from 1 to 10,000. Note the remarkably chaotic, unpredictable movement of this function.
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If this file is freely licensed, but otherwise unsuitable for Commons (e.g. out of
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Please ensure that the file has a properly descriptive and unambiguous name
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This licensing tag was added to this file as part of the GFDL
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74:(SVG file, nominally 600 × 480 pixels, file size: 26 KB) 527:|reason=<Why it can't be moved>}} 271: 214: 162: 106: 156:The green lines above and below provide a limit of 90:, with the leading terms subtracted, for values of 305: 251: 185: 145: 785:Creative Commons Attribution-ShareAlike 3.0 files 571:This file was suggested for transfer by a bot ( 428:https://creativecommons.org/licenses/by-sa/3.0/ 470:Any user may perform this transfer; refer to 186:{\displaystyle \pm {\frac {1}{2}}{\sqrt {x}}} 8: 197:in 1903 shows that, for some real, positive 790:Knowledge (XXG) license migration completed 252:{\displaystyle \psi (x)-x<-K{\sqrt {x}}} 41:Size of this PNG preview of this SVG file: 757: 600: 306:{\displaystyle \psi (x)-x>K{\sqrt {x}}} 510:Endorse this file for transfer by adding 463:This file is a candidate to be copied to 296: 270: 242: 213: 176: 166: 161: 105: 759: 729: 472:Knowledge (XXG):Moving files to Commons 764:Produced by GNUPLOT 4.0 patchlevel 0 497:transfer it; repeat violators may be 146:{\displaystyle \psi (x)-x+\log(\pi )} 7: 97:More precisely, this is a graph of 578:. Please verify that this file is 750: 79: 67: 512:|human=<your username> 562: 455: 401:This work is licensed under the 393: 388: 382: 347: 21: 719:You cannot overwrite this file. 477:If this file has problems with 14: 367:GNU Free Documentation License 357:GNU Free Documentation License 341:, Linas Vepstas, 3 July 2006 281: 275: 224: 218: 140: 134: 116: 110: 26: 1: 445:, with the following markup: 31: 806: 425:Attribution-ShareAlike 3.0 406:Attribution-ShareAlike 3.0 557: 328:Chebyshev function to 10M 16: 704:== Summary == Graph of 703: 660: 582:before transferring it. 742:File:Chebyshev-big.svg 525:Do not move to Commons 329: 307: 253: 201:, there are values of 187: 147: 327: 308: 254: 188: 148: 580:suitable for Commons 269: 212: 160: 104: 61:2,560 × 2,048 pixels 57:1,280 × 1,024 pixels 737:User:Linas/Pictures 47:Other resolutions: 732:Chebyshev function 706:Chebyshev function 669:16:33, 3 July 2006 626:18:03, 3 July 2006 545:transferring; see 505:Other Instructions 489:for Commons, then 485:, or is otherwise 330: 316:infinitely often. 303: 249: 183: 143: 88:Chebyshev function 768: 767: 715: 590: 589: 586: 585: 514:to this Template. 465:Wikimedia Commons 434: 433: 377: 376: 301: 247: 181: 174: 797: 758: 701: 700: 681: 661:with limit lines 658: 657: 638: 577: 566: 565: 559: 538: 528: 513: 459: 452: 430: 429: 426: 423: 418: 415:licensing update 403:Creative Commons 397: 392: 386: 379: 371: 368: 365: 351: 344: 312: 310: 309: 304: 302: 297: 258: 256: 255: 250: 248: 243: 192: 190: 189: 184: 182: 177: 175: 167: 152: 150: 149: 144: 75: 64: 53:960 × 768 pixels 49:300 × 240 pixels 43:600 × 480 pixels 805: 804: 800: 799: 798: 796: 795: 794: 770: 769: 746: 728: 721: 716: 690: 689: 687: 679: 647: 646: 644: 636: 592: 591: 569: 563: 553: 552: 532: 522: 511: 506: 450: 439: 427: 424: 421: 420: 412: 410: 387: 373: 369: 366: 363: 335: 322: 267: 266: 210: 209: 158: 157: 102: 101: 84: 77: 73: 66: 65: 46: 12: 11: 5: 803: 801: 793: 792: 787: 782: 772: 771: 766: 765: 762: 749: 745: 744: 739: 734: 726: 725: 724: 717: 714: 713: 702: 685: 682: 676: 671: 666: 663: 662: 659: 642: 639: 633: 628: 623: 619: 618: 615: 612: 609: 606: 603: 596: 595: 588: 587: 584: 583: 567: 555: 554: 551: 550: 539: 529: 519:Commons' scope 515: 507: 504: 503: 501:from editing. 460: 447: 438: 435: 432: 431: 398: 375: 374: 361: 352: 334: 331: 321: 318: 314: 313: 300: 295: 292: 289: 286: 283: 280: 277: 274: 260: 259: 246: 241: 238: 235: 232: 229: 226: 223: 220: 217: 195:Erhard Schmidt 180: 173: 170: 165: 154: 153: 142: 139: 136: 133: 130: 127: 124: 121: 118: 115: 112: 109: 83: 80: 78: 40: 36: 35: 34: 29: 24: 19: 13: 10: 9: 6: 4: 3: 2: 802: 791: 788: 786: 783: 781: 778: 777: 775: 763: 760: 756: 753: 747: 743: 740: 738: 735: 733: 730: 722: 720: 711: 707: 698: 694: 688: 683: 677: 675: 672: 670: 667: 665: 664: 655: 651: 645: 640: 634: 632: 629: 627: 624: 621: 620: 616: 613: 610: 607: 604: 602: 601: 599: 593: 581: 576: 574: 568: 561: 560: 556: 548: 544: 540: 536: 530: 526: 520: 516: 509: 508: 502: 500: 496: 493:this tag and 492: 488: 484: 480: 475: 474:for details. 473: 467: 466: 461: 458: 454: 453: 446: 444: 441:Created with 436: 419: 416: 409: 407: 404: 399: 396: 391: 385: 381: 380: 372: 359: 358: 353: 350: 346: 345: 342: 340: 332: 326: 319: 317: 298: 293: 290: 287: 284: 278: 272: 265: 264: 263: 244: 239: 236: 233: 230: 227: 221: 215: 208: 207: 206: 204: 200: 196: 178: 171: 168: 163: 137: 131: 128: 125: 122: 119: 113: 107: 100: 99: 98: 95: 93: 89: 81: 76: 71: 70:Original file 62: 58: 54: 50: 44: 39: 33: 30: 28: 25: 23: 20: 18: 15: 754: 751: 718: 597: 594:File history 570: 549:for details. 542: 533:{{ 523:{{ 494: 490: 476: 469: 462: 449:linewidth 2 440: 422:Cc-by-sa-3.0 411: 400: 362: 355: 336: 315: 261: 202: 198: 155: 96: 91: 85: 68: 22:File history 761:Image title 479:attribution 437:Source code 337:Created by 780:GFDL files 774:Categories 723:File usage 710:User:Linas 678:600 × 480 635:600 × 480 611:Dimensions 535:Keep local 487:ineligible 339:User:Linas 205:such that 27:File usage 608:Thumbnail 605:Date/Time 573:User:Fbot 483:copyright 408:License. 333:Licensing 285:− 273:ψ 237:− 228:− 216:ψ 164:± 138:π 132:⁡ 120:− 108:ψ 86:Graph of 748:Metadata 697:contribs 654:contribs 320:See also 32:Metadata 680:(16 KB) 637:(26 KB) 622:current 617:Comment 499:blocked 443:gnuplot 82:Summary 72:‎ 543:before 495:DO NOT 491:remove 686:Linas 643:Linas 262:and 693:talk 650:talk 614:User 468:. 364:GFDL 291:> 234:< 17:File 129:log 776:: 695:| 652:| 481:, 59:| 55:| 51:| 45:. 699:) 691:( 656:) 648:( 575:) 417:. 299:x 294:K 288:x 282:) 279:x 276:( 245:x 240:K 231:x 225:) 222:x 219:( 203:x 199:K 179:x 172:2 169:1 141:) 135:( 126:+ 123:x 117:) 114:x 111:( 92:n 63:.

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File:Chebyshev.svg
600 × 480 pixels
300 × 240 pixels
960 × 768 pixels
1,280 × 1,024 pixels
2,560 × 2,048 pixels
Original file
Chebyshev function
Erhard Schmidt

User:Linas
GFDL
GNU Free Documentation License



Creative Commons
Attribution-ShareAlike 3.0
licensing update
gnuplot
Copy to Commons
Wikimedia Commons
Knowledge (XXG):Moving files to Commons
attribution
copyright
ineligible

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