Extensions of the classical transformations of the hypergeometric function F23

Robert S. Maier

doi:10.1016/j.aam.2019.01.002

Extensions of the classical transformations of the hypergeometric function F23

Robert S. Maier

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

It is shown that the classical quadratic and cubic transformation identities satisfied by the hypergeometric function F23 can be extended to include additional parameter pairs, which differ by integers. In the extended identities, which involve hypergeometric functions of arbitrarily high order, the added parameters are nonlinearly constrained: in the quadratic case, they are the negated roots of certain orthogonal polynomials of a discrete argument (dual Hahn and Racah ones). Specializations and applications of the extended identities are given, including an extension of Whipple's identity relating very well poised F67(1) series and balanced F34(1) series, and extensions of other summation identities.

Original language	English (US)
Pages (from-to)	25-47
Number of pages	23
Journal	Advances in Applied Mathematics
Volume	105
DOIs	https://doi.org/10.1016/j.aam.2019.01.002
State	Published - Apr 2019

Keywords

Discrete orthogonal polynomial
Generalized hypergeometric function
Hypergeometric transformation
Summation identity

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2019.01.002

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AB - It is shown that the classical quadratic and cubic transformation identities satisfied by the hypergeometric function F23 can be extended to include additional parameter pairs, which differ by integers. In the extended identities, which involve hypergeometric functions of arbitrarily high order, the added parameters are nonlinearly constrained: in the quadratic case, they are the negated roots of certain orthogonal polynomials of a discrete argument (dual Hahn and Racah ones). Specializations and applications of the extended identities are given, including an extension of Whipple's identity relating very well poised F67(1) series and balanced F34(1) series, and extensions of other summation identities.

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KW - Generalized hypergeometric function

KW - Hypergeometric transformation

KW - Summation identity

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ER -

Extensions of the classical transformations of the hypergeometric function F23

Abstract

Keywords

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