129:
874:
231:
33:
74:
701:
538:
756:
refers to the imaginary axis, which indicates the integral is carried out along a straight line parallel to the imaginary axis lying to the right of all the singularities of the following expression:
549:
814:
92:
754:
403:
731:
146:
46:
427:
915:
241:
299:
193:
271:
165:
954:
439:
278:
172:
52:
325:
212:
110:
60:
285:
179:
939:
908:
267:
256:
161:
150:
934:
696:{\displaystyle V(j,t)={\frac {1}{2\pi i}}\int _{a_{0}-i\infty }^{a_{0}+i\infty }e^{tp}{\frac {V^{\ast }(j,p)}{p}}\,dp}
901:
139:
944:
762:
292:
186:
406:
881:
343:
949:
359:
347:
248:
351:
850:
825:
736:
885:
373:
709:
17:
430:
412:
928:
230:
128:
873:
355:
533:{\displaystyle V^{\ast }(j,p)=p\int _{0}^{\infty }V(j,t)e^{-pt}\,dt}
854:
224:
122:
67:
26:
889:
433:
variable. The
Laplace–Carson transform is defined as:
252:
88:
847:
Vibration of solids and structures under moving loads
765:
739:
712:
552:
442:
415:
376:
153:. Unsourced material may be challenged and removed.
83:
may be too technical for most readers to understand
808:
748:
725:
695:
532:
421:
397:
358:and engineering, particularly in the field of
354:with significant applications in the field of
909:
8:
257:introducing citations to additional sources
61:Learn how and when to remove these messages
916:
902:
809:{\displaystyle e^{tp}{\frac {V(j,t)}{p}}}
779:
770:
764:
738:
717:
711:
686:
659:
652:
643:
622:
617:
601:
596:
574:
551:
543:The inverse Laplace–Carson transform is:
523:
511:
483:
478:
447:
441:
414:
375:
326:Learn how and when to remove this message
213:Learn how and when to remove this message
111:Learn how and when to remove this message
95:, without removing the technical details.
247:Relevant discussion may be found on the
837:
93:make it understandable to non-experts
7:
870:
868:
151:adding citations to reliable sources
888:. You can help Knowledge (XXG) by
743:
634:
613:
484:
25:
42:This article has multiple issues.
872:
240:relies largely or entirely on a
229:
127:
72:
31:
138:needs additional citations for
50:or discuss these issues on the
797:
785:
677:
665:
568:
556:
504:
492:
465:
453:
392:
380:
1:
955:Mathematical analysis stubs
733:is a real-valued constant,
971:
867:
268:"Laplace–Carson transform"
162:"Laplace–Carson transform"
845:Frýba, Ladislav (1973).
749:{\displaystyle i\infty }
340:Laplace–Carson transform
18:Laplace-Carson transform
940:Differential equations
884:–related article is a
810:
750:
727:
697:
534:
423:
399:
398:{\displaystyle V(j,t)}
882:mathematical analysis
811:
751:
728:
726:{\displaystyle a_{0}}
698:
535:
424:
400:
763:
737:
710:
550:
440:
413:
374:
344:Pierre Simon Laplace
338:In mathematics, the
253:improve this article
147:improve this article
935:Integral transforms
638:
488:
360:railway engineering
348:John Renshaw Carson
806:
746:
723:
693:
592:
530:
474:
419:
395:
352:integral transform
897:
896:
826:Laplace transform
804:
684:
590:
422:{\displaystyle p}
336:
335:
328:
318:
317:
303:
223:
222:
215:
197:
121:
120:
113:
65:
16:(Redirected from
962:
945:Fourier analysis
918:
911:
904:
876:
869:
859:
858:
842:
815:
813:
812:
807:
805:
800:
780:
778:
777:
755:
753:
752:
747:
732:
730:
729:
724:
722:
721:
702:
700:
699:
694:
685:
680:
664:
663:
653:
651:
650:
637:
627:
626:
616:
606:
605:
591:
589:
575:
539:
537:
536:
531:
522:
521:
487:
482:
452:
451:
428:
426:
425:
420:
404:
402:
401:
396:
331:
324:
313:
310:
304:
302:
261:
233:
225:
218:
211:
207:
204:
198:
196:
155:
131:
123:
116:
109:
105:
102:
96:
76:
75:
68:
57:
35:
34:
27:
21:
970:
969:
965:
964:
963:
961:
960:
959:
925:
924:
923:
922:
865:
863:
862:
844:
843:
839:
834:
822:
781:
766:
761:
760:
735:
734:
713:
708:
707:
655:
654:
639:
618:
597:
579:
548:
547:
507:
443:
438:
437:
411:
410:
372:
371:
368:
332:
321:
320:
319:
314:
308:
305:
262:
260:
246:
234:
219:
208:
202:
199:
156:
154:
144:
132:
117:
106:
100:
97:
89:help improve it
86:
77:
73:
36:
32:
23:
22:
15:
12:
11:
5:
968:
966:
958:
957:
952:
947:
942:
937:
927:
926:
921:
920:
913:
906:
898:
895:
894:
877:
861:
860:
836:
835:
833:
830:
829:
828:
821:
818:
817:
816:
803:
799:
796:
793:
790:
787:
784:
776:
773:
769:
745:
742:
720:
716:
704:
703:
692:
689:
683:
679:
676:
673:
670:
667:
662:
658:
649:
646:
642:
636:
633:
630:
625:
621:
615:
612:
609:
604:
600:
595:
588:
585:
582:
578:
573:
570:
567:
564:
561:
558:
555:
541:
540:
529:
526:
520:
517:
514:
510:
506:
503:
500:
497:
494:
491:
486:
481:
477:
473:
470:
467:
464:
461:
458:
455:
450:
446:
418:
394:
391:
388:
385:
382:
379:
367:
364:
342:, named after
334:
333:
316:
315:
251:. Please help
237:
235:
228:
221:
220:
135:
133:
126:
119:
118:
80:
78:
71:
66:
40:
39:
37:
30:
24:
14:
13:
10:
9:
6:
4:
3:
2:
967:
956:
953:
951:
948:
946:
943:
941:
938:
936:
933:
932:
930:
919:
914:
912:
907:
905:
900:
899:
893:
891:
887:
883:
878:
875:
871:
866:
856:
852:
848:
841:
838:
831:
827:
824:
823:
819:
801:
794:
791:
788:
782:
774:
771:
767:
759:
758:
757:
740:
718:
714:
690:
687:
681:
674:
671:
668:
660:
656:
647:
644:
640:
631:
628:
623:
619:
610:
607:
602:
598:
593:
586:
583:
580:
576:
571:
565:
562:
559:
553:
546:
545:
544:
527:
524:
518:
515:
512:
508:
501:
498:
495:
489:
479:
475:
471:
468:
462:
459:
456:
448:
444:
436:
435:
434:
432:
416:
408:
389:
386:
383:
377:
365:
363:
361:
357:
353:
349:
345:
341:
330:
327:
312:
301:
298:
294:
291:
287:
284:
280:
277:
273:
270: –
269:
265:
264:Find sources:
258:
254:
250:
244:
243:
242:single source
238:This article
236:
232:
227:
226:
217:
214:
206:
195:
192:
188:
185:
181:
178:
174:
171:
167:
164: –
163:
159:
158:Find sources:
152:
148:
142:
141:
136:This article
134:
130:
125:
124:
115:
112:
104:
94:
90:
84:
81:This article
79:
70:
69:
64:
62:
55:
54:
49:
48:
43:
38:
29:
28:
19:
890:expanding it
879:
864:
846:
840:
705:
542:
369:
339:
337:
322:
306:
296:
289:
282:
275:
263:
239:
209:
200:
190:
183:
176:
169:
157:
145:Please help
140:verification
137:
107:
98:
82:
58:
51:
45:
44:Please help
41:
950:Transforms
929:Categories
832:References
366:Definition
279:newspapers
173:newspapers
47:improve it
855:70-151037
744:∞
661:∗
635:∞
614:∞
608:−
594:∫
584:π
513:−
485:∞
476:∫
449:∗
309:June 2024
249:talk page
203:June 2024
101:June 2024
53:talk page
820:See also
407:function
350:, is an
431:complex
356:physics
293:scholar
187:scholar
87:Please
853:
706:where
295:
288:
281:
274:
266:
189:
182:
175:
168:
160:
880:This
405:be a
300:JSTOR
286:books
194:JSTOR
180:books
886:stub
851:LCCN
409:and
370:Let
346:and
272:news
166:news
255:by
149:by
91:to
931::
849:.
429:a
362:.
56:.
917:e
910:t
903:v
892:.
857:.
802:p
798:)
795:t
792:,
789:j
786:(
783:V
775:p
772:t
768:e
741:i
719:0
715:a
691:p
688:d
682:p
678:)
675:p
672:,
669:j
666:(
657:V
648:p
645:t
641:e
632:i
629:+
624:0
620:a
611:i
603:0
599:a
587:i
581:2
577:1
572:=
569:)
566:t
563:,
560:j
557:(
554:V
528:t
525:d
519:t
516:p
509:e
505:)
502:t
499:,
496:j
493:(
490:V
480:0
472:p
469:=
466:)
463:p
460:,
457:j
454:(
445:V
417:p
393:)
390:t
387:,
384:j
381:(
378:V
329:)
323:(
311:)
307:(
297:·
290:·
283:·
276:·
259:.
245:.
216:)
210:(
205:)
201:(
191:·
184:·
177:·
170:·
143:.
114:)
108:(
103:)
99:(
85:.
63:)
59:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.