Multiple Integrals Involving A Extension of The Hurwitz-Lerch Zeta Function, Class of Pol,Ynomials, Multivariable I-Function, Multivariable Aleph-Function and Product of Two Jacobi Polynomials

F.Y.Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V54P515

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 54 | Number 2 | Year 2018 | Article Id. IJMTT-V54P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V54P515

Multiple Integrals Involving A Extension of The Hurwitz-Lerch Zeta Function, Class of Pol,Ynomials, Multivariable I-Function, Multivariable Aleph-Function and Product of Two Jacobi Polynomials

F.Y.Ayant

Citation :

F.Y.Ayant, "Multiple Integrals Involving A Extension of The Hurwitz-Lerch Zeta Function, Class of Pol,Ynomials, Multivariable I-Function, Multivariable Aleph-Function and Product of Two Jacobi Polynomials," International Journal of Mathematics Trends and Technology (IJMTT), vol. 54, no. 2, pp. 138-145, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V54P515

Abstract

In the present paper we evaluate the multiple integrals involving the product of a multivariable Aleph-function, a extension of the Hurwitz-Lerch Zeta function, the multivariable I-function defined by Prasad [2], the product of two Jacobi polynomials 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

Multivariable Aleph-function, general class of polynomials, multiple integral, extension of the Hurwitz-Lerch Zeta function, multivariable I-function, multivariable H-function, Jacobi polynomial

References

[1]Marichev O.I. Prudnikov A.P. And Brychkow Y.A. Elementay functions. Integrals and series Vol 2. USSR Academy of sciences . Moscow 1986.
[2] Y.N. Prasad , Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 ( 1986 ) , page 231-237.
[3] Sharma C.K.and Ahmad S.S.: On the multivariable I-function. Acta ciencia Indica Math , 1994 vol 20,no2, p 113- 116.
[4] 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.
[5] 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.
[6] H.M. Srivastava, R.K. Saxena, T.K. Pogány, R. Saxena, Integral and computational representations of the extended Hurwitz–Lerch zeta function, Integr.Transf. Spec. Funct. 22 (2011) 487–506