Selberg integral involving the sequence of functions,a class of pol,ynomials , a multivariable I-function and a multivariable A-function

F.Y. AY ANT

doi:https://doi.org/10.14445/22315373/IJMTT-V41P511

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 41 | Number 2 | Year 2017 | Article Id. IJMTT-V41P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V41P511

Selberg integral involving the sequence of functions,a class of pol,ynomials , a multivariable I-function and a multivariable A-function

F.Y. AY ANT

Abstract

In the present paper we evaluate the modified Selberg integral involving the product of a multivariable A-function defined by Gautam et al [4], a sequence of functions, the multivariable I-function defined by Nambisan et al [5] and a general class of polynomials of several variables. The importance of the result established in this paper lies in the fact they involve the A-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.We will study two particular cases.

Keywords

Multivariable A-function, general class of polynomials, modified Selberg integral, sequence of functions , multivariable I-function, multivariable H-function.

References

[1] Agrawal B.D. And Chaubey J.P. Certain derivation of generating relations for generalized polynomials. Indian J.Pure and Appl. Math 10 (1980), page 1155-1157, ibid 11 (1981), page 357-359.
[2] Andrew G.G and Askey R. Special function. Cambridge. University. Press 1999.
[3] Fujiwara I. A unified presentation of classical orthogonal polynomials. Math. Japon. 11 (1966), page133-148.
[4] 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.
[5] 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.
[6] Raizada S.K. A study of unified representation of special functions of Mathematics Physics and their use in statistical and boundary value problem. Ph.D. Thesis, Bundelkhand University, Jhansi, India, 1991.
[7] Salim T.O. A serie formula of generalized class of polynomials associated with Laplace transform and fractional integral operators. J. Rajasthan. Acad. Phy. Sci. 1(3) (2002), page 167-176.
[8] 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.
[9] 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.
[10] 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, "Selberg integral involving the sequence of functions,a class of pol,ynomials , a multivariable I-function and a multivariable A-function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 41, no. 2, pp. 127-136, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V41P511