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Probl. Anal. Issues Anal., 2019, Volume 8(26), Issue 1, Pages 47–64 (Mi pa257)  

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.

Funding Agency Grant Number
Russian Science Foundation 14-11-00022
This research has been supported by the Russian Science Foundation under project 14-11-00022.


DOI: https://doi.org/10.15393/j3.art.2019.5210

Full text: PDF file (487 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.58, 517.96
MSC: 33D15, 26A51
Received: 21.08.2018
Revised: 30.12.2018
Accepted:10.01.2019
Language:

Citation: S. I. Kalmykov, D. B. Karp, “Inequalities for some basic hypergeometric functions”, Probl. Anal. Issues Anal., 8(26):1 (2019), 47–64

Citation in format AMSBIB
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\by S.~I.~Kalmykov, D.~B.~Karp
\paper Inequalities for some basic hypergeometric functions
\jour Probl. Anal. Issues Anal.
\yr 2019
\vol 8(26)
\issue 1
\pages 47--64
\mathnet{http://mi.mathnet.ru/pa257}
\crossref{https://doi.org/10.15393/j3.art.2019.5210}
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\elib{http://elibrary.ru/item.asp?id=37104075}


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