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Inequalities for some basic hypergeometric functions
S. I. Kalmykovab, D. B. Karpab a Far Eastern Federal University,
8 Sukhanova St., Vladivostok, 690090, Russia
b Institute of Applied Mathematics, FEBRAS, 7 Radio St., Vladivostok, 690041, Russia
Abstract:
We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric functions
with respect to the 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 Turánian formed by a particular case of Heine's basic hypergeometric function.
Its $q=1$ case also appears to be new.
Keywords:
basic hypergeometric function, log-convexity, log-concavity, multiplicative concavity, generalized Turánian, $q$-hypergeometric identity.
Received: 21.08.2018 Revised: 30.12.2018 Accepted: 10.01.2019
Citation:
S. I. Kalmykov, D. B. Karp, “Inequalities for some basic hypergeometric functions”, Probl. Anal. Issues Anal., 8(26):1 (2019), 47–64
Linking options:
https://www.mathnet.ru/eng/pa257 https://www.mathnet.ru/eng/pa/v26/i1/p47
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Abstract page: | 185 | Full-text PDF : | 74 | References: | 26 |
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