Some monotonicity properties and inequalities for Γ and ζ - functions

Valmir Krasniqi; Toufik Mansour; Armend Sh Shabani

Some monotonicity properties and inequalities for Γ and ζ - functions

Valmir Krasniqi, Toufik Mansour, Armend Sh Shabani

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper several monotonicity properties and inequalities are given for Γ and Γ_q functions as well as for their logarithmic derivatives ψ and ψ_q A p analogue of Riemann Zeta function ζ_p is introduced. Using the generalization of Schwarz inequality and Holder's inequality some inequalities relating ζ, ζ_p, Γ and Γ_p are obtained. By the use of Laplace Convolution Theorem, some monotonicity results related to digamma function ψ and its derivatives of order n are obtained. For the Γ_p-function, defined by Euler, some properties related to monotonicity are given. Also, some properties of a p analogue of the ψ function have been established.

Original language	English
Pages (from-to)	365-376
Number of pages	12
Journal	Mathematical Communications
Volume	15
Issue number	2
State	Published - Dec 2010

Keywords

Gamma function
Psi function
Zeta function

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Applied Mathematics

Cite this

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AU - Krasniqi, Valmir

AU - Mansour, Toufik

AU - Shabani, Armend Sh

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N2 - In this paper several monotonicity properties and inequalities are given for Γ and Γq functions as well as for their logarithmic derivatives ψ and ψq A p analogue of Riemann Zeta function ζp is introduced. Using the generalization of Schwarz inequality and Holder's inequality some inequalities relating ζ, ζp, Γ and Γp are obtained. By the use of Laplace Convolution Theorem, some monotonicity results related to digamma function ψ and its derivatives of order n are obtained. For the Γp-function, defined by Euler, some properties related to monotonicity are given. Also, some properties of a p analogue of the ψ function have been established.

AB - In this paper several monotonicity properties and inequalities are given for Γ and Γq functions as well as for their logarithmic derivatives ψ and ψq A p analogue of Riemann Zeta function ζp is introduced. Using the generalization of Schwarz inequality and Holder's inequality some inequalities relating ζ, ζp, Γ and Γp are obtained. By the use of Laplace Convolution Theorem, some monotonicity results related to digamma function ψ and its derivatives of order n are obtained. For the Γp-function, defined by Euler, some properties related to monotonicity are given. Also, some properties of a p analogue of the ψ function have been established.

KW - Gamma function

KW - Psi function

KW - Zeta function

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M3 - Article

AN - SCOPUS:79551639011

SN - 1331-0623

VL - 15

SP - 365

EP - 376

JO - Mathematical Communications

JF - Mathematical Communications

IS - 2

ER -

Some monotonicity properties and inequalities for Γ and ζ - functions

Abstract

Keywords

ASJC Scopus subject areas

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