A Ramanujan's hypergeometric transformation formula, its validity range and implications

2024/11/29 by M. A. Shpot, Shpot, M. A.
Mathematics · Social Sciences · #Advanced Mathematical Identities #Religion and Sociopolitical Dynamics in Nigeria #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.2411.19608

Abstract

We extend the validity range of a Ramanujan's hypergeometric transformation formula proved by Berndt, Bhargava and Garvan, Trans. Amer. Math. Soc. 347, 4163 (1995) and study its implications. Relations to special values of complete elliptic integrals of the first kind in the singular value theory are established. Consequently, we derive several closed-form evaluations of hypergeometric functions ₂F₁ with different sets of parameters and arguments. Connections with other hypergeometric transformations and some recent results are discussed.

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