An Integral Involving Generalized Multivariable
Mittag-Leffler Function

Vandana Agarwal; Monika Malhotra

doi:https://doi.org/10.14445/22315373/IJMTT-V65I6P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 6 | Year 2019 | Article Id. IJMTT-V65I6P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I6P503

An Integral Involving Generalized Multivariable Mittag-Leffler Function

Vandana Agarwal , Monika Malhotra

Abstract

The aim of the present paper is to establish new integrals involving generalized multivariable Mittag-Leffler function Erpjj,,lj,B,pj,qj (Z)associated with a general class of polynomials. The integral obtained is unified in nature and act as key formula from which we can obtain as their special cases, integral formulae concerning a large number of simpler special functions and polynomials. For the sake of illustration, we record here three corollaries as special cases of our main formula which are also new and of interest by themselves. The findings of the present results are basic in nature and are likely to find useful applications in several fields

Keywords

Multivariable Mittag-Leffler Function

References

[1] A.A. Kilbas, M. Siago and R.K. Saxena, Generalized Mittag-Leffler function and generalized fractional calculus operators,Integral Transforms Spec. Funct. , Vol. 15, (2004), pp. 31-49.
[2] M.K. Gujar, J.C. Prajapati and K. Gupta, A study of generalized Mittag Leffler function via Fractional Calculus, Journal of Inequalities and Special Functions, 5, No. (2014), 6-13.
[3] G. M. Mittag-Leffler, Sur la nouvelle function Eα(x), C. R. Acad. Sci. Paris No 137 (1903), 554-558.
[4] T. R. Prabhakar,A singular integral equation with a generalized Mittag-Leffler function in the Kernel, Yokohama Math. J. No 19 (1971) 7-15. MR0293349 (45#2426).Zbl 0221.45003.
[5] T.O. Salim and A.W. Faraj, A generalization of Mittag-Leffler function and integral operator associated with fractional calculus, J. of Fract. Calc. and Appl., 3 (2012), 1-13.
[6] A.K. Shukla and J.C. Prajapati,On a generalization of Mittag-Leffler function and its properties, Math. Anal. Appl., 336 (2007), 797-811.
[7] H.M. Srivastava, A Contour inyegral involving Fox’s H-function, Indian J.Math. 14(1972), 1-6.
[8] H.M. Srivastava and H.L. Manocha, A Treatise on Generating Functions, Elli’s Horwood Ltd. Chichester, John Wileyand Sons,New York 1984.
[9] G. Szego,Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ. Vol. 23 (1975), Fourth edition, Amer. Math. Soc.Providence, Rhode Island.
[10] A. Wiman, Uber de fundamental satz in der theorie der funktionen Eα(x), Acta Math. No. 29 (1905), 191-201.MR1555014.JFM36.0471.01

Citation :

Vandana Agarwal , Monika Malhotra, "An Integral Involving Generalized Multivariable Mittag-Leffler Function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 6, pp. 15-20, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I6P503