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Journal of Applied Mathematics and Computation

ISSN Print: 2576-0645 Downloads: 156028 Total View: 1854599
Frequency: quarterly ISSN Online: 2576-0653 CODEN: JAMCEZ
Email: jamc@hillpublisher.com
Article Open Access http://dx.doi.org/10.26855/jamc.2024.12.002

Application of Parseval’s Theorem with K-Functions

Iyaya Wanjala, Sitawa Wattanga*, George Mocheche

Mathematics Department, Multimedia University of Kenya, Nairobi 15653-00503, Kenya.

*Corresponding author: Sitawa Wattanga

Published: January 20,2025

Abstract

In this paper, we introduce the concept of the k-gamma function, ᴦk (x), detailing its definitions and key properties. We also explore the k-Pochhammer symbol (∝)k,n, highlighting its relationship to the classical Pochhammer symbol, (∝)n. Further, we introduce the k-Bessel function, Jk,v(x) and the k-Gauss hypergeometric function, along with the k-Legendre duplication formula, ᴦ(n+1/2). By closely analysing these concepts, we sought to establish a foundational framework for the theory of k-special functions, whose basis was the formulation of the k-gamma function. Our focus was the derivation of some results that could be useful for researchers working in the development of the in-depth theory of k-special functions motivated by the formulation of the k-gamma function. Obtained results are meant to enhance the mathematical understanding of k-special functions and their applications. The insights gained from this study may contribute to advancing theoretical and applied aspects of mathematical analysis and special functions that will significantly contribute to the understanding of k-special functions and their potential applications in different mathematical disciplines.

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How to cite this paper

Application of Parseval's Theorem with K-Functions

How to cite this paper: Iyaya Wanjala, Sitawa Wattanga, George Mocheche. (2024) Application of Parseval's Theorem with K-FunctionsJournal of Applied Mathematics and Computation8(4), 286-295.

DOI: http://dx.doi.org/10.26855/jamc.2024.12.002