Integral involving a generalized multiple-index Mittag-Leffler function, Bessel functions, a class of polynomials multivariable Aleph-function and multivariable I-function

F.Y.Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V53P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 1 | Year 2018 | Article Id. IJMTT-V53P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P503

Integral involving a generalized multiple-index Mittag-Leffler function, Bessel functions, a class of polynomials multivariable Aleph-function and multivariable I-function

F.Y.Ayant

Abstract

In the present paper we evaluate a general integral involving the product of a generalized multiple-index Mittag-Leffler function,product of three Bessel functions, multivariable Aleph-function, the multivariable I-function defined by Prasad [6] and general class of polynomials of several variables. The importance of the result established in this paper lies in the fact they involve the Aleph-function of several variables which is sufficiently general in nature and capable to yielding a large of results merely by specializating the parameters their in.

Keywords

Multivariable Aleph-function, general class of polynomials, generalized multiple-index Mittag-Leffler function, multivariable I-function, multivariable H-function

References

[1] Appell P. (1880). "Sur les séries hypergéométriques de deux variables et sur des équations différentielles linéaires aux dérivées partielles". Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French). 90: 296– 298 and 731–735. JFM 12.0296.01. (see also "Sur la série F3(α,α',β,β',γ; x,y)" in C. R. Acad. Sci. 90, pp. 977– 980).
[2] Appell, Paul (1882). Sur les fonction hypergeometric à deux variables. Journal de Mathématiques pures et appliquées. (3ème série) (in French). 8: 173–216.
[3]Gradshteyn I.S and Ryzhik I.N. Tables of integrals, series and products, Fourth ed. Academic. Press. New York (1980).
[4] J. Paneva-Konovska, Multi-index (3m-parametric) Mittag-Leffler functions and fractional calculus.Compt. Rend. de l’Acad. Bulgare des Sci. 64, No 8 (2011), page 1089–1098.
[5] T. R. Prabhakar, A singular integral equation with a generalizedMittag-Leffler function in the kernel.Yokohama Math. J.19(1971), page 7–15.
[6] Y.N. Prasad , Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 ( 1986 ) , page 231-237.
[7] Sharma C.K.and Ahmad S.S.: On the multivariable I-function. Acta ciencia Indica Math , 1994 vol 20,no2, p 113- 116.
[8] Srivastava H.M. A multilinear generating function for the Konhauser set of biorthogonal polynomials suggested by Laguerre polynomial, Pacific. J. Math. 177(1985), page183-191.
[9] H.M. Srivastava And R.Panda. Some expansion theorems and generating relations for the H-function of several complex variables. Comment. Math. Univ. St. Paul. 24(1975), p.119-137.

Citation :

F.Y.Ayant, "Integral involving a generalized multiple-index Mittag-Leffler function, Bessel functions, a class of polynomials multivariable Aleph-function and multivariable I-function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 1, pp. 13-21, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P503