A New Representation of the k-Gamma Functions

Asifa Tassaddiq
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Asifa Tassaddiq: College of Computer and Information Sciences, Majmaah University, Majmaah 11952, Saudi Arabia

Mathematics, 2019, vol. 7, issue 2, 1-13

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.

Keywords: series representation; gamma function; k-gamma function; k-Pochhammer symbol; delta functions; Fourier transform; test functions; distributions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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