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Some completely monotonic functions associated with the q-gamma and the q-polygamma functions

Author name : Eid Sayed K Sayed
Publication Date : 2015-07-30
Journal Name : Acta Mathematica Scientia

Abstract

In this paper, the q-analogue of the Stirling formula for the q-gamma function (Moak formula) is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma functions for all real number q > 0. The monotonicity of these functions is used to establish sharp inequalities for the q-gamma and the q-polygamma functions and the q-Harmonic number. Our results are shown to be a generalization of results which were obtained by Selvi and Batir [23].

Keywords

the q-analogue - Stirling formula - q-polygamma functions

Publication Link

https://doi.org/10.1016/S0252-9602(15)30050-3

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