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arXiv · 1808.05105

Inequalities for some basic hypergeometric functions

S. I. Kalmykov·D. B. Karp
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Abstract

We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shift of all its parameters. For a particular case of Heine's basic hypergeometric function we prove logarithmic concavity and convexity with respect to the bottom parameter. We further establish a linearization identity for the generalized Tur\'{a}nian formed by a particular case of Heine's basic hypergeometric function. Its $q=1$ case also appears to be new.

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S. I. Kalmykov, D. B. Karp. 2018-08-15. Inequalities for some basic hypergeometric functions. https://arxiv.org/abs/1808.05105

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