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.
Highlights
Diaz and Pariguan [1] introduced and investigated k-gamma functions when they were evaluatingFeynman integrals
It is remarkable that k-gamma functions and related k-Pochhammer symbols are more the functions of the fractional calculus
The elementary functions like Sine, Cosine, Hyperbolic Sine and Cosine are some examples of distributions in D 0 whose Fourier transforms being delta function are in Z 0
Summary
Diaz and Pariguan [1] introduced and investigated k-gamma functions when they were evaluating. By taking inspiration from the above discussion, in our current investigation, we acquire a new representation for the k-gamma functions in terms of complex delta functions by following the methodology of Chaudhry & Qadir [15], Tassaddiq & Qadir [16,17], Tassaddiq [18], Lail & Qadir [19], Tassaddiq et al [20] and Tassaddiq [21,22].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
