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

DOI:
https://doi.org/10.1090/S0002-9939-1990-1036991-1

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 Ramanujanâs celebrated Notebooks; it also serves to solve the problem posed by R. J. Evans [5].

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Additional Information

Keywords:
Hypergeometric functions,
boundary value problems,
Euler-Darboux equation,
analytic continuation,
asymptotic formula,
Kampé de Fériet series

Article copyright:
© Copyright 1990
American Mathematical Society