Abstract
Motivated essentially by the success of applications of the Mittag-Leffler function and its generalizations in science and engineering and -calculus, we propose here a unification of certain -generalizations of the Mittag-Leffler function including -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 -Konhauser polynomial is considered for which the series inequality relations and inverse series relations are obtained.
Citation
Bharti V. Nathwani. Rajesh V. Savalia. Cynthia V. Rodrigues. Harshal S. Gharat. "GENERALIZED -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