FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
On transformations of hypergeometric functions with integer parameter differences |
Bakhtin K.E., Prilepkina E.G. |
2025, issue 2, P. 261–270 DOI: https://doi.org/10.47910/FEMJ202520 |
Abstract |
| Several facts concerning transformations and summations of hypergeometric functions with integral parametric differences have been proven. A new summation formula complementing the well-known Karlsson–Minton summation formula has been established. A new three–term relation has been derived from the first Miller–Paris transformation. It is shown how the second Miller–Paris transformation can be obtained by induction from the Euler–Pfaff transformation, and a recursive formula for the representing polynomial is provided. An integral representation of Meijer's G-function, which underlies the second Miller–Paris transformation, has been established. |
Keywords: generalized hypergeometric function, summation formulas, hypergeometric identity, Miller–Paris transformations. |
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References |
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