On a unified integral formula involving multivariable I-functions and classes of polynomials

F.Y.Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V53P517

International Journal of Mathematics Trends and Technology

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Volume 53 | Number 2 | Year 2018 | Article Id. IJMTT-V53P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P517

On a unified integral formula involving multivariable I-functions and classes of polynomials

F.Y.Ayant

Abstract

In this paper we evaluate a unified and general finite integral involves the product of the multivariable I-functions defined by Prathima and Nambisan [1] and the general classes of multivariable polynomials with general arguments. On account of the most general nature of the functions and the classes of the polynomials and their general arguments occuring in our main integral, several new and known integrals follow as its simple specials cases. We shall study the particular case concerning the multivariable H-function defined by Srivastava et al [6,7],the Srivastava-Daoust polynomial [4] and the I-function of two variables defined by Rathie et al [2].

Keywords

Multivariable I-function, general class of multivariable polynomials, multivariable H-function, I-function of two variables

References

[1] Prathima J. Nambisan V. and Kurumujji S.K. A Study of I-function of Several Complex Variables, International Journalof Engineering Mathematics Vol (2014) , 2014 page 1-12.
[2] Rathie A.K. Kumari K.S. and Vasudevan Nambisan T.M. A study of I-functions of two variables. Le Matematiche Vol 64 (1), page 285-305.
[3] 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.
[4] Srivastava H.M. and Daoust M.C. Certain generalized Neumann expansions associated with Kampé de Fériet function. Nederl. Akad. Wetensch. Proc. Ser A72 = Indag Math 31(1969) page 449-457.
[5] Srivastava H.M. And Garg M. Some integral involving a general class of polynomials and multivariable H-function. Rev. Roumaine Phys. 32 (1987), page 685-692.
[6] Srivastava H.M., Gupta K.C. and Goyal S.P. The H-functions of one and two variables with applications. South Asian Publishers, New Delhi, Madras, 1982.
[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, "On a unified integral formula involving multivariable I-functions and classes of polynomials," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 2, pp. 141-150, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P517