553:
862:
22:
886:
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744:
205:
387:
142:. The concept not necessarily unique or well-defined, but the general idea is to find a formula for a series and then evaluate it outside its
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927:
325:"An Analogy Between Transients and Mathematical Sequences and Some Nonlinear Sequence-to-Sequence Transforms Suggested by It. Part 1"
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961:
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43:
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305:
215:
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32:
814:
636:
36:
476:
423:
893:
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242:
143:
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794:
631:
400:
8:
774:
641:
135:
275:
704:
615:
600:
572:
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491:
175:
87:
804:
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577:
531:
521:
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486:
352:
300:
901:
789:
610:
536:
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408:
344:
139:
567:
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290:
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458:
443:
324:
270:
940:
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348:
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511:
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127:
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21:
396:
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745:
1/2 + 1/3 + 1/5 + 1/7 + 1/11 + ⋯ (inverses of primes)
735:
1 − 1 + 2 − 6 + 24 − 120 + ⋯ (alternating factorials)
245:
251:
938:
921:
381:
828:Hypergeometric function of a matrix argument
684:1 + 1/2 + 1/3 + ... (Riemann zeta function)
343:. Cambridge University Press. p. 542.
50:. Unsourced material may be challenged and
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914:
388:
374:
149:
740:1 + 1/2 + 1/3 + 1/4 + ⋯ (harmonic series)
236:1 + 1/2 + 1/3 + 1/4 + ⋯ (harmonic series)
114:Learn how and when to remove this message
395:
939:
322:
369:
880:
338:
312:can also be used on divergent series
48:adding citations to reliable sources
15:
705:1 − 1 + 1 − 1 + ⋯ (Grandi's series)
176:1 − 1 + 1 − 1 + ⋯ (Grandi's series)
13:
14:
978:
823:Generalized hypergeometric series
884:
861:
860:
833:Lauricella hypergeometric series
551:
20:
843:Riemann's differential equation
341:Practical Extrapolation Methods
332:Naval Ordnance Lab White Oak Md
310:Van Wijngaarden transformation
1:
838:Modular hypergeometric series
679:1/4 + 1/16 + 1/64 + 1/256 + ⋯
339:Sidi, Avram (February 2010).
316:
900:. You can help Knowledge by
206:1 − 1 + 2 − 6 + 24 − 120 + …
7:
967:Mathematical analysis stubs
848:Theta hypergeometric series
264:
10:
983:
879:
730:Infinite arithmetic series
674:1/2 + 1/4 + 1/8 + 1/16 + ⋯
669:1/2 − 1/4 + 1/8 − 1/16 + ⋯
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349:10.1017/CBO9780511546815
296:Mittag-Leffler summation
561:Properties of sequences
323:Shanks, Daniel (1949).
252:{\displaystyle \gamma }
150:Common divergent series
134:is the equivalent of a
896:–related article is a
424:Arithmetic progression
253:
962:Mathematical analysis
894:mathematical analysis
815:Hypergeometric series
429:Geometric progression
306:Euler–Boole summation
254:
144:radius of convergence
957:Sequences and series
795:Trigonometric series
587:Properties of series
434:Harmonic progression
243:
44:improve this article
952:Summability methods
775:Formal power series
573:Monotonic function
492:Fibonacci sequence
281:Lindelöf summation
249:
909:
908:
874:
873:
805:Generating series
753:
752:
725:1 − 2 + 4 − 8 + ⋯
720:1 + 2 + 4 + 8 + ⋯
715:1 − 2 + 3 − 4 + ⋯
710:1 + 2 + 3 + 4 + ⋯
700:1 + 1 + 1 + 1 + ⋯
650:
649:
578:Periodic sequence
547:
546:
532:Triangular number
522:Pentagonal number
502:Heptagonal number
487:Complete sequence
409:Integer sequences
301:Lambert summation
262:
261:
226:1 − 2 + 4 − 8 + ⋯
216:1 + 2 + 4 + 8 + ⋯
196:1 − 2 + 3 − 4 + ⋯
186:1 + 2 + 3 + 4 + ⋯
166:1 + 1 + 1 + 1 + ⋯
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790:Dirichlet series
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527:Polygonal number
507:Hexagonal number
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367:
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335:
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276:Cesàro summation
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140:divergent series
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56:
24:
16:
982:
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937:
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809:
758:Kinds of series
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688:
655:Explicit series
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620:
582:
568:Cauchy sequence
556:
543:
497:Figurate number
474:
468:
459:Powers of three
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394:
359:
327:
319:
291:Borel summation
286:Euler summation
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244:
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152:
120:
109:
103:
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57:
55:
41:
25:
12:
11:
5:
980:
970:
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964:
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933:
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906:
889:
872:
871:
869:
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845:
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835:
830:
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819:
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811:
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800:Fourier series
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792:
787:
785:Puiseux series
782:
780:Laurent series
777:
772:
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750:
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722:
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634:
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622:
621:
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588:
584:
583:
581:
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570:
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541:
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336:
318:
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298:
293:
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273:
271:Abel summation
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211:
210:0.59634736...
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122:
121:
28:
26:
19:
9:
6:
4:
3:
2:
979:
968:
965:
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948:
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931:
926:
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919:
917:
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911:
905:
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867:
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844:
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836:
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831:
829:
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824:
821:
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796:
793:
791:
788:
786:
783:
781:
778:
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766:
765:Taylor series
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762:
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723:
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664:
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630:
629:
627:
623:
617:
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612:
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592:
589:
585:
579:
576:
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571:
569:
566:
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559:
554:
538:
535:
534:
533:
530:
528:
525:
523:
520:
518:
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510:
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500:
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495:
493:
490:
488:
485:
484:
482:
478:
471:
465:
462:
460:
457:
455:
454:Powers of two
452:
450:
447:
445:
442:
440:
439:Square number
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435:
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421:
419:
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402:
398:
391:
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384:
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371:
368:
360:
358:9780511546815
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246:
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104:December 2022
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68:
65: –
64:
60:
59:Find sources:
53:
49:
45:
39:
38:
34:
29:This article
27:
23:
18:
17:
902:expanding it
891:
876:
770:Power series
512:Lucas number
464:Powers of 10
444:Cubic number
340:
331:
131:
125:
110:
101:
91:
84:
77:
70:
58:
42:Please help
30:
637:Conditional
625:Convergence
616:Telescoping
601:Alternating
517:Pell number
128:mathematics
63:"Antilimit"
941:Categories
662:Convergent
606:Convergent
317:References
160:Antilimit
74:newspapers
693:Divergent
611:Divergent
473:Advanced
449:Factorial
397:Sequences
247:γ
132:antilimit
31:does not
866:Category
632:Absolute
265:See also
642:Uniform
88:scholar
52:removed
37:sources
594:Series
401:series
355:
190:-1/12
157:Series
138:for a
130:, the
90:
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76:
69:
61:
892:This
537:array
417:Basic
328:(PDF)
170:-1/2
136:limit
95:JSTOR
81:books
898:stub
477:list
399:and
353:ISBN
308:and
230:1/3
200:1/4
180:1/2
67:news
35:any
33:cite
345:doi
220:-1
126:In
46:by
943::
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102:(
92:·
85:·
78:·
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54:.
40:.
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