Version 1
: Received: 31 July 2024 / Approved: 31 July 2024 / Online: 31 July 2024 (15:34:23 CEST)
How to cite:
Singh, P. Integral Forms and Connections of Multi-Parameter Mittag-Leffler Functions with Fox-Wright and Hypergeometric Functions. Preprints2024, 2024072614. https://doi.org/10.20944/preprints202407.2614.v1
Singh, P. Integral Forms and Connections of Multi-Parameter Mittag-Leffler Functions with Fox-Wright and Hypergeometric Functions. Preprints 2024, 2024072614. https://doi.org/10.20944/preprints202407.2614.v1
Singh, P. Integral Forms and Connections of Multi-Parameter Mittag-Leffler Functions with Fox-Wright and Hypergeometric Functions. Preprints2024, 2024072614. https://doi.org/10.20944/preprints202407.2614.v1
APA Style
Singh, P. (2024). Integral Forms and Connections of Multi-Parameter Mittag-Leffler Functions with Fox-Wright and Hypergeometric Functions. Preprints. https://doi.org/10.20944/preprints202407.2614.v1
Chicago/Turabian Style
Singh, P. 2024 "Integral Forms and Connections of Multi-Parameter Mittag-Leffler Functions with Fox-Wright and Hypergeometric Functions" Preprints. https://doi.org/10.20944/preprints202407.2614.v1
Abstract
In this study, the complex interactions between the well-known Mittag-Leffler functions with two, three, and four parameters are explored. We first study the integral forms of the Mittag-Leffler function $\mathsf{E}_{\alpha, \beta}^{\rho,\kappa}(z)$ with the goal of clarifying its mathematical behaviours and features. Moreover, we create relations between these functions and generalised hypergeometric functions and Fox-Wright functions, expanding the range of their use and comprehension. We explore a number of unique situations by in-depth examination, providing insight into the subtle characteristics of these functions. This investigation advances our theoretical knowledge and opens up possibilities for future applications in a number of scientific fields. As such, this study adds to the current conversation in mathematical analysis and is an important tool for both practitioners and researchers.
Keywords
Mittag-Leffler functions, Wright hypergeometric functions, Fox-Wright function, generalized hypergeometric function
Subject
Computer Science and Mathematics, Mathematics
Copyright:
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.
