J Austral Math Soc Ser A 57 pp281--294, 1994.

The Behaviour of the Fourth Type of Lauricella's Hypergeometric Series in n Variables Near the Boundaries of its Convergence Region

Megumi Saigo and H. M. Srivastava

Abstract

For Lauricella's hypergeometric function F_D⁽ⁿ⁾ of n variables, we prove two formulas exhibiting its behaviour near the boundaries of the n-dimensional region of convergence of the multiple series defining it. Each of these results can be applied to deduce the corresponding properties of several simpler hypergeometric functions of one, two and more variables.

1991 AMS Subject Classification: primary 35B40, 33C65; secondary 33B15

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Authors

Megumi Saigo

Department of Applied Mathematics, Fukuoka University, Fukuoka 814-01, Japan.

H. M. Srivastava

Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada.