## 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 |
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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