On general Eulerian integral of certain products of A-function, the multivariable I-function and a class of polynomials

F.Y. AY ANT

doi:https://doi.org/10.14445/22315373/IJMTT-V41P509

International Journal of Mathematics Trends and Technology

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Volume 41 | Number 1 | Year 2017 | Article Id. IJMTT-V41P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V41P509

On general Eulerian integral of certain products of A-function, the multivariable I-function and a class of polynomials

F.Y. AY ANT

Abstract

The object of this paper is to establish an general Eulerian integral involving the product of the A-function defined by Gautam et al [1], the multivariable I-function defined by Nambisan et al [2], a general class of multivariable polynomials and a generalized hypergeometric function which provide unification and extension of numerous results. We will study the particular case concerning the multivariable H-function defined by Srivastava et al [8] and the Srivastava-Daoust polynomial [5].

Keywords

Eulerian integral, multivariable I-function, Lauricella function of several variables, multivariable A-function, generalized hypergeometric function, multivariable H-function.

References

[1] Gautam B.P., Asgar A.S. and Goyal A.N. On the multivariable A-function. Vijnana Parishas Anusandhan Patrika Vol 29(4) 1986, page 67-81.
[2] Prathima J. Nambisan V. and Kurumujji S.K. A Study of I-function of Several Complex Variables, International Journal of Engineering Mathematics Vol(2014) , 2014 page 1-12.
[3] Saigo M. and Saxena R.K. Unified fractional integral formulas for the multivariable H-function I. J.Fractional Calculus 15 (1999), page 91-107.
[4] Saigo M. and Saxena R.K. Unified fractional integral formulas for the multivariable H-function III. J.Fractional Calculus 20 (2001), page 45-68.
[5] 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.
[6] 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.
[7] Srivastava H.M. and Karlsson P.W. Multiple Gaussian Hypergeometric series. Ellis.Horwood. Limited. New-York, Chichester. Brisbane. Toronto , 1985.
[8] 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. AY ANT, "On general Eulerian integral of certain products of A-function, the multivariable I-function and a class of polynomials," International Journal of Mathematics Trends and Technology (IJMTT), vol. 41, no. 1, pp. 103-114, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V41P509