Two-Sided Inequalities for Generalized Hypergeometric Function

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Karp, D and Sitnik, S. M (2007) Two-Sided Inequalities for Generalized Hypergeometric Function. Research report collection, 10 (2).

Abstract

We find two-sided inequalities for the generalized hypergeometric function with positive parameters restricted by certain additional conditions. Inequalities are derived as corollaries of a theorem asserting the monotony of the quotient of two generalized hypergeometric functions with shifted parameters. The proofs hinge on a generalized Stieltjes representation of the generalized hypergeometric function. In the last section of the paper we list some open questions and conjectures.

Item type Article
URI https://vuir.vu.edu.au/id/eprint/18363
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords generalized hypergeometric function, generalized Stieltjes function, hypergeometric inequality, Thomae relations
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