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The behavior of the zero-balanced hypergeometric series ${}_ pF_ {p-1}$ near the boundary of its convergence region

Authors: Megumi Saigo and H. M. Srivastava
Journal: Proc. Amer. Math. Soc. 110 (1990), 71-76
MSC: Primary 33C20
MathSciNet review: 1036991
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Abstract: For a zero-balanced generalized hypergeometric function $_p{F_{p - 1}}\left ( z \right )$, the authors prove a formula exhibiting its behavior near the boundary point $z = 1$ of the region of convergence of the series defining it. The result established here provides an interesting extension of a formula which appeared in one of Ramanujan’s celebrated Notebooks; it also serves to solve the problem posed by R. J. Evans [5].

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Keywords: Hypergeometric functions, boundary value problems, Euler-Darboux equation, analytic continuation, asymptotic formula, Kampé de Fériet series
Article copyright: © Copyright 1990 American Mathematical Society