Triple integral involving a generalized multiple-index Mittag-Leffler function, a class of polynomials multivariable Aleph-function and multivariable I-function I

F.Y.Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V53P513

International Journal of Mathematics Trends and Technology

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Volume 53 | Number 2 | Year 2018 | Article Id. IJMTT-V53P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P513

Triple integral involving a generalized multiple-index Mittag-Leffler function, a class of polynomials multivariable Aleph-function and multivariable I-function I

F.Y.Ayant

Abstract

In the present paper we evaluate a general triple integral involving the product of a generalized multiple-index Mittag-Leffler function, multivariable Aleph-function, the multivariable I-function defined by Prasad [4] 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]Marichev O.I. Prudnikov A.P. And Brychkow Y.A. Elementay functions. Integrals and series Vol 1. USSR Academy of sciences . Moscow 1986.
[2] 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.
[3] T. R. Prabhakar, A singular integral equation with a generalizedMittag-Leffler function in the kernel.Yokohama Math. J.19(1971), page 7–15.
[4] Y.N. Prasad , Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 ( 1986 ) , page 231-237.
[5] Sharma C.K.and Ahmad S.S.: On the multivariable I-function. Acta ciencia Indica Math , 1994 vol 20,no2, p 113- 116.
[6] 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.
[7] 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, "Triple integral involving a generalized multiple-index Mittag-Leffler function, a class of polynomials multivariable Aleph-function and multivariable I-function I," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 2, pp. 104-111, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P513