Inequalities for series in q-shifted factorials and q-gamma functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:460

Article

Kalmykov, S. I.^1,2,3  Karp, D. B.^2,3 

[1] Shanghai Jiao Tong Univ, Shanghai, Peoples R China

[2] Far Eastern Fed Univ, Vladivostok, Russia

[3] FEBRAS, Inst Appl Math, Vladivostok, Russia

关键词: q-Gamma function;    Basic hypergeometric function;    Log-convexity;    Log-concavity;    Generalized Turanian;    q-Hypergeometric identity;   

DOI  :  10.1016/j.jmaa.2017.11.041

来源: Elsevier

【 摘 要 】

The paper studies logarithmic convexity and concavity of power series with coefficients involving q-gamma functions or q-shifted factorials with respect to a parameter contained in their arguments. The principal motivating examples of such series are basic hypergeometric functions. We consider four types of series. For each type we establish conditions sufficient for the power series coefficients of the generalized Turanian formed by these series to have constant sign. Finally, we furnish seven examples of basic hypergeometric functions satisfying our general theorems. This investigation extends our previous results on power series with coefficient involving the ordinary gamma functions and the shifted factorials. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free