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Some new inequalities for the -gamma and related functions

Jozsef Sandor|MOHAMED EL BACHRAOUI
장전수학회 (Jangjeon Mathematical Society)|2019.07|Advanced Studies in Contemporary Mathematics|제29권 제3호|pp. 293-310

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참고문헌

키워드

convexityinequalitiesspecial functionsq-gamma functionq-digamma functionmono- tonicity
주제분류수학

초록

We consider convexity and monotonicity properties for some func- tions related to the q-gamma function. As applications, we give a variety of inequalities for the q-gamma function, the q-digamma function q(x), and the q-series. Among other consequences, we improve a result of Alzer and Grinsh- pan about the zeros of the function q(x). We use q-analogues for the Gauss multiplication formula to put in closed form members of some of our inequal- ities.

Abstract

We consider convexity and monotonicity properties for some func- tions related to the q-gamma function. As applications, we give a variety of inequalities for the q-gamma function, the q-digamma function q(x), and the q-series. Among other consequences, we improve a result of Alzer and Grinsh- pan about the zeros of the function q(x). We use q-analogues for the Gauss multiplication formula to put in closed form members of some of our inequal- ities.

참고문헌 (23)

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