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Mathematics 2019, 7(2), 133; https://doi.org/10.3390/math7020133

A New Representation of the k-Gamma Functions

College of Computer and Information Sciences, Majmaah University, Majmaah 11952, Saudi Arabia
Received: 8 December 2018 / Revised: 16 January 2019 / Accepted: 19 January 2019 / Published: 1 February 2019
(This article belongs to the Special Issue Special Functions and Applications)
Full-Text   |   PDF [288 KB, uploaded 12 February 2019]

Abstract

The products of the form z ( z + l ) ( z + 2 l ) ( z + ( k 1 ) l ) are of interest for a wide-ranging audience. In particular, they frequently arise in diverse situations, such as computation of Feynman integrals, combinatory of creation, annihilation operators and in fractional calculus. These expressions can be successfully applied for stated applications by using a mathematical notion of k-gamma functions. In this paper, we develop a new series representation of k-gamma functions in terms of delta functions. It led to a novel extension of the applicability of k-gamma functions that introduced them as distributions defined for a specific set of functions. View Full-Text
Keywords: series representation; gamma function; k-gamma function; k-Pochhammer symbol; delta functions; Fourier transform; test functions; distributions series representation; gamma function; k-gamma function; k-Pochhammer symbol; delta functions; Fourier transform; test functions; distributions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Tassaddiq, A. A New Representation of the k-Gamma Functions. Mathematics 2019, 7, 133.

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