Generalized Extended Confluent, Whittaker $k$-functions and Their Properties

Authors

  • Syed Ali Haider Shah Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
  • Mujahid Hussain Shah Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
  • Miguel Vivas-Cortez Escuela de Ciencias F\'{i}sicas y Matem\'{a}ticas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Cat\'{o}lica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador
  • Shahid Mubeen Department of Mathematics, Baba Guru Nanak University, Nankana Sahib 3900, Pakistan
  • Gauhar Rahman Department of Mathematics \& Statistics, Hazara University, Mansehra 21300, Pakistan

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6279

Keywords:

Gamma $k$-function, Beta $k$-function, Whittaker $k$-function, Hankel transform, Mellin transform

Abstract

The main objective of this research paper is to explore  further generalization of confluent hypergeometric and Whittaker functions by introducing a new parameter $k>0$, in generalized extended confluent hypergeometric and Whittaker functions defined by Khan \emph{et al.} \cite{m7}. We also investigate some properties such as integral representations, Mallin transforms, Hankel, Laplace transformations and derivative of these new generalized extended confluent hypergeometric and Whittaker $k$-functions. We also obtain Riemann-Liouville fractional integral and Riemann-Liouville $k$-fractional integral of these new generalized extended Whittaker $k$-function.

Downloads

Published

2025-08-03

Issue

Vol. 18 No. 3: (July 2025)

Section

Mathematical Physics

License

Copyright (c) 2025 Syed Ali Haider Shah, Mujahid Hussain Shah, Miguel Vivas-Cortez, Shahid Mubeen, Gauhar Rahman

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Generalized Extended Confluent, Whittaker $k$-functions and Their Properties. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6279. https://doi.org/10.29020/nybg.ejpam.v18i3.6279