A generalization of Kummer's identity
| dc.creator | Vidunas, Raimundas | |
| dc.date | 2000-05-10 | |
| dc.date | 2000-10-31 | |
| dc.date.accessioned | 2026-07-07T04:35:09Z | |
| dc.date.available | 2026-07-07T04:35:09Z | |
| dc.description | The well-known Kummer's formula evaluates the hypergeometric series 2F1(A,B;C;-1) when the relation B-A+C=1 holds. This paper deals with evaluation of 2F1(-1) series in the case when C-A+B is an integer. Such a series is expressed as a sum of two Γ-terms multiplied by terminating 3F2(1) series. A few such formulas were essentially known to Whipple in 1920's. Here we give a simpler and more complete overview of this type of evaluations. Additionally, algorithmic aspects of evaluating hypergeometric series are considered. We illustrate Zeilberger's method and discuss its applicability to non-terminating series, and present a couple of similar generalizations of other known formulas. | |
| dc.description | 13 pages; classical proofs simplified, possible transformations reviewed; in the algoritmic part similar evaluations of other series added | |
| dc.identifier | https://arxiv.org/abs/math/0005095 | |
| dc.identifier | http://arxiv.org/abs/math/0005095 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59162 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 33C05, 33F10, 39A10 | |
| dc.title | A generalization of Kummer's identity | |
| dc.type | text |