Inequalities concerning the
-gamma and
-polygamma functions
Abstract
In this paper, we establish several inequalities involving the
-gamma and
-polygamma functions. Among other tools, we employ the mean value therorem, the Hermite-Hadamard's inequality, Petrovic's inequality and the Holder's inequality. Upon some parameter variations, we recover some known results as special cases of the established results.
![(p,k)](http://212.189.136.205/plugins/generic/latexRender/cache/dcb7957de54504cd1d9d701c140d024f.png)
![(p,k)](http://212.189.136.205/plugins/generic/latexRender/cache/dcb7957de54504cd1d9d701c140d024f.png)
DOI Code:
10.1285/i15900932v38n2p93
Keywords:
$(p,k)$-gamma function; $(p,k)$-digamma function; $(p,k)$-polygamma functions; inequality
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