A generalization of Kummer's identity
| Authors |
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| Publication date |
2000
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| Publisher |
s.n.
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| Organisations |
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Faculty of Science (FNWI) - Korteweg-de Vries Institute for Mathematics (KdVI)
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| Abstract |
The well-known Kummer's formula evaluates the hypergeometric series ${}_2F_1(A,B;C;-1)$ when the relation $B-A+C=1$ holds. In this paper a formula is presented which evaluates this series in case when $B-A+C$ is an integer. The formula expresses the infinite series as a linear combination of two $\Gamma$-terms with coefficients being finite hypergeometric ${}_3F_2$ series. The generalized formula basically follows from the results of Whipple. A complete proof is given using Zeilberger's method and contiguous relations. Algorithmical problems of summation of this kind of series are considered.
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| Document type |
Working paper
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