Original scientific paper

Some monotonicity properties and inequalities for $\Gamma$ and $\zeta$ - functions

Valmir Krasniqi ; Department of Mathematics, University of Prishtina, Prishtinë, Republic of Kosova
Toufik Mansour ; Department of Mathematics, University of Haifa, Haifa, Israel
Armend Sh. Shabani ; Department of Mathematics, University of Prishtina, Prishtinë, Republic of Kosova

Abstract

In this paper several monotonicity properties and inequalities are given for $\Gamma$ and $\Gamma_q$ functions as well as for their logarithmic derivatives $\psi$ and $\psi_q$. A $p$ analogue of Riemann Zeta function $\zeta_p$ is introduced. Using the generalization of Schwarz inequality and Holder's inequality some inequalities relating $\zeta, \zeta_p, \Gamma$ and $\Gamma_p$ are obtained. By the use of Laplace Convolution Theorem, some monotonicity results related to digamma function $\psi$ and its derivatives of order $n$ are obtained. For the $\Gamma_p$-function, defined by Euler, some properties related to monotonicity are given. Also, some properties of a $p$ analogue of the $\psi$ function have been established.

Keywords

gamma function; psi function; zeta function

Hrčak ID:

61841

URI

https://hrcak.srce.hr/61841

Publication date:

8.12.2010.

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