Dirichlet Averages of Generalized Multi–indexMittag–Leffler Functions

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Dirichlet Averages of Generalized Multi–indexMittag–Leffler Functions Ram Saxena

The object of this article is to investigate the Dirichlet averages of the generalized multi–index Mittag–Leffler functions introduced by Saxena and Nishimoto [23, 24]. Representationsof such relations are obtained in terms of Riemann–Liouville integrals and hypergeometricfunctions of several variables. Some interesting special cases of the established results as-sociated with generalized Mittag–Leffler functions due to Srivastava and Tomovski [32] andmulti–index Mittag–Leffler functions due to Kiryakova [12] are deduced. Certain resultsgiven earlier by Kilbaset al.[8] also follow as special cases of our findings.

DOI: https://armjmath.sci.am/index.php/ajm/article/view/79 Armenian Journal of Mathematics, 3(4) 174-187

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Keywords

Generalized Mittag–Leffler Function, Dirichlet Averages, Riemann–LiouvilleFractional Integral, Multi–index Mittag–Leffler Function, Srivastava–Daoust GeneralizedLauricellaFDHypergeometric Function

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