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http://dx.doi.org/10.7858/eamj.2019.004

CERTAIN FORMULAS INVOLVING A MULTI-INDEX MITTAG-LEFFLER FUNCTION  

Bansal, Manish Kumar (Department of Mathematics, Govt. Engineering College)
Harjule, P. (Department of Mathematics, Malaviya National Institute of Technology)
Choi, Junesang (Department of Mathematics, Dongguk University)
Mubeen, Shahid (Department of Mathematics, University of Sargodha)
Kumar, Devendra (Department of Mathematics, JECRC University)
Publication Information
East Asian mathematical journal / v.35, no.1, 2019 , pp. 23-30 More about this Journal
Abstract
Since Mittag-Leffler introduced the so-called Mittag-Leffler function, a number of its extensions have been investigated due mainly to their applications in a variety of research subjects. Shukla and Prajapati presented a lot of formulas involving a generalized Mittag-Leffler function in a systematic manner. Motivated mainly by Shukla and Prajapati's work, we aim to investigate a generalized multi-index Mittag-Leffler function and, among possible numerous formulas, choose to present several formulas involving this generalized multi-index Mittag-Leffler function such as a recurrence formula, derivative formula, three integral transformation formulas. The results presented here, being general, are pointed out to reduce to yield relatively simple formulas including known ones.
Keywords
Gamma function; beta function; Mittag-Leffler function; generalized Mittag-Leffler functions; Generalized multi-index Mittag-Leffler function; Fox-Wright hypergeometric function; Laplace transform; Euler transform; Whittaker transform;
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