Dirichlet Averages of Generalized Mittag-Leffler Type Function
Abstract
:1. Introduction and Preliminaries
2. The Generalized Mittag-Leffler Type Function (the R-Function)
- (i)
- converges for , if ,
- (ii)
- converges for , if , and
- (iii)
- diverges for all if .
- (a)
- absolutely convergent for , if ,
- (b)
- conditionally convergent for , if , and
- (c)
- divergent for , if .
3. Bivariate Dirichlet Averages
4. Dirichlet Average Expressed in Terms of Srivastava–Daoust Function
5. Multivariate Dirichlet Averages
6. Concluding Remarks
- Express (possibly) the Srivastava–Daoust generalization (17) of the Lauricella hypergeometric function in terms of the multivariate H-function;
- Express (possibly) the right members of Theorems 3 and 4 in terms of the multivariate H-function.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
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Kumar, D.; Ram, J.; Choi, J. Dirichlet Averages of Generalized Mittag-Leffler Type Function. Fractal Fract. 2022, 6, 297. https://doi.org/10.3390/fractalfract6060297
Kumar D, Ram J, Choi J. Dirichlet Averages of Generalized Mittag-Leffler Type Function. Fractal and Fractional. 2022; 6(6):297. https://doi.org/10.3390/fractalfract6060297
Chicago/Turabian StyleKumar, Dinesh, Jeta Ram, and Junesang Choi. 2022. "Dirichlet Averages of Generalized Mittag-Leffler Type Function" Fractal and Fractional 6, no. 6: 297. https://doi.org/10.3390/fractalfract6060297