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

Saigo, Megumi; Srivastava, H. M.

doi:10.1090/S0002-9939-1990-1036991-1

The behavior of the zero-balanced hypergeometric series ${}_ pF_ {p-1}$ near the boundary of its convergence region
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Proc. Amer. Math. Soc. 110 (1990), 71-76 Request permission

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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On a property of the Appell hypergeometric function

12

On properties of the Appell hypergeometric functions

and

and the generalized Gauss function

66

On properties of the Lauricella hypergeometric function

104

On properties of hypergeometric functions of three variables

and

37

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The behavior of the Lauricella hypergeometric series

in

variables near the boundaries of its convergence region

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