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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 1 | Year 2018 | Article Id. IJMTT-V53P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P509

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


F.Y.Ayant
Abstract

In the present paper we evaluate a general integral involving the product of the extension of the generalized multiple-index Mittag-Leffler function, product of two Bessel functions and product of two the multivariable I-functions 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
general class of polynomials, generalized multiple-index Mittag-Leffler function, multivariable I-function, multivariable H-function, Bessel function.
References

[1] Luke Y.K. Bessel functions . Midwest. Research. Institute.Kansas City. Missouri (1962).
[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] 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.
[6] 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 the extension of the generalized multiple-index Mittag-Leffler function,Bessel functions, a class of polynomials and multivariable I-functions I," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 1, pp. 68-75, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P509

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