October 2024 GENERALIZED k-MITTAG-LEFFLER FUNCTION AND ITS PROPERTIES
Bharti V. Nathwani, Rajesh V. Savalia, Cynthia V. Rodrigues, Harshal S. Gharat
Rocky Mountain J. Math. 54(5): 1427-1446 (October 2024). DOI: 10.1216/rmj.2024.54.1427

Abstract

Motivated essentially by the success of applications of the Mittag-Leffler function and its generalizations in science and engineering and k-calculus, we propose here a unification of certain k-generalizations of the Mittag-Leffler function including k-generalizations of the Saxena–Nishimoto function, the Bessel–Maitland function, the Dotsenko function, the elliptic function, etc. We obtain the order and type, asymptotic estimate, a differential equation, eigenfunction property and double series relation for the proposed unification. As a specialization, a generalized k-Konhauser polynomial is considered for which the series inequality relations and inverse series relations are obtained.

Citation

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Bharti V. Nathwani. Rajesh V. Savalia. Cynthia V. Rodrigues. Harshal S. Gharat. "GENERALIZED k-MITTAG-LEFFLER FUNCTION AND ITS PROPERTIES." Rocky Mountain J. Math. 54 (5) 1427 - 1446, October 2024. https://doi.org/10.1216/rmj.2024.54.1427

Information

Received: 14 October 2022; Revised: 16 February 2023; Accepted: 4 May 2023; Published: October 2024
First available in Project Euclid: 26 September 2024

MathSciNet: MR4800635
zbMATH: 07941312
Digital Object Identifier: 10.1216/rmj.2024.54.1427

Subjects:
Primary: 33B15 , 33C47 , 33E12 , 33E99

Keywords: Differential equation , eigenfunction , k-Gamma function , k-Pochhammer symbol

Rights: Copyright © 2024 Rocky Mountain Mathematics Consortium

Vol.54 • No. 5 • October 2024
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