Inequalities for some basic hypergeometric functions

• Main Authors: Kalmykov S. I., Karp D. B.
• Format: Article
• Language: English
• Published: Petrozavodsk State University 2019-01-01
• Series: Проблемы анализа
• Subjects: basic hypergeometric function; log-convexity; log-concavity; multiplicative concavity; generalized Turanian; q-hypergeometric identity
• Online Access: http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=5210&lang=ru

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.