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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The behavior of the zero-balanced hypergeometric series $ {}\sb pF\sb {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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1036991-1
PII: S 0002-9939(1990)1036991-1
Keywords: Hypergeometric functions, boundary value problems, Euler-Darboux equation, analytic continuation, asymptotic formula, Kampé de Fériet series
Article copyright: © Copyright 1990 American Mathematical Society