On general Eulerian integral of certain product of Kumari's multivariable I-function
the classes of polynomials and generalized hypergeometric function

F.Y. Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V43P519

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 43 | Number 2 | Year 2017 | Article Id. IJMTT-V43P519 | DOI : https://doi.org/10.14445/22315373/IJMTT-V43P519

On general Eulerian integral of certain product of Kumari's multivariable I-function the classes of polynomials and generalized hypergeometric function

F.Y. Ayant

Abstract

The object of this paper is to establish an general Eulerian integral involving the product of the multivariable I-function defined by Kumari et al [2], the general classes 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 [9] and the Srivastava-Daoust polynomial [6].

Keywords

Eulerian integral, multivariable I-function, Lauricella function of several variables, multivariable H-function, generalized hypergeometric function. 2010 Mathematics Subject Classification. 33C45, 33C60, 26D20

References

[1] B. L. J. Braaksma, “Asymptotic expansions and analytic continuations for a class of Barnes integrals,”Compositio Mathematical, vol. 15, pp. 239–341, 1964.
[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. A multilinear generating function for the Konhauser set of biorthogonal polynomials suggested by Laguerre polynomial, Pacific. J. Math. 177(1985), page183-191.
[6] 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.
[7] 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.
[8] Srivastava H.M. and Karlsson P.W. Multiple Gaussian Hypergeometric series. Ellis.Horwood. Limited. New-York, Chichester. Brisbane. Toronto , 1985.
[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, "On general Eulerian integral of certain product of Kumari's multivariable I-function the classes of polynomials and generalized hypergeometric function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 43, no. 2, pp. 135-145, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V43P519