Inequalities for some basic hypergeometric functions
Journal Title: Проблемы анализа-Issues of Analysis - Year 2019, Vol 8, Issue 1
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.
Authors and Affiliations
S. Kalmykov, D. Karp
THE THEOREM ON EXISTENCE OF SINGULAR SOLUTIONS TO NONLINEAR EQUATIONS
The aim of this paper is to present some applications of pregularity theory to investigations of nonlinear multivalued mappings. The main result addresses to the problem of existence of solutions to nonlinear equations i...
ЛИНЕЙНО-ИНВАРИАНТНЫЕ СЕМЕЙСТВА ГОЛОМОРФНЫХ ОТОБРАЖЕНИЙ ШАРА, ПЕРЕХОД К ВЫСШИМ РАЗМЕРНОСТЯМ
In the paper there has been given the complete proof of an extension theorem from [1], which concerns the changes of the order of linearly invariant families (LIF) during passage from arbitrarily fixed LIF in C^n to a LI...
COEFFICIENT INEQUALITY FOR MULTIVALENT BOUNDED TURNING FUNCTIONS OF ORDER α
The objective of this paper is to obtain the sharp upper bound to the H_2(p + 1), second Hankel determinant for p-valent (multivalent) analytic bounded turning functions (also called functions whose derivatives have posi...
СВОЙСТВО ВЫПУКЛОСТИ ВЗАИМНЫХ МУЛЬТИФРАКТАЛЬНЫХ РАЗМЕРНОСТЕЙ
В работе установлено свойство выпуклости взаимной муль- тифрактальной упаковочной размерности подмножества пере- сечения носителей вероятностых борелевских мер µ и ν. Также показано, что взаимная мультифрактальная хаусдо...
FAMILIES OF ELLIPTIC FUNCTIONS AND UNIFORMIZATION OF COMPLEX TORI WITH A UNIQUE POINT OVER INFINITY
We investigate the problem of describing a one-parametric family of elliptic functions which uniformizes a given family of ramified coverings of the Riemann sphere with maximal possible ramification over infinity. We fin...