Generalized finite integral involving the extension of Zeta-function, a general class of polynomials,the multivariable Aleph-function,the multivariable I-function and elliptic integral of the first kind

F.Y.Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V46P524

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 46 | Number 3 | Year 2017 | Article Id. IJMTT-V46P524 | DOI : https://doi.org/10.14445/22315373/IJMTT-V46P524

Generalized finite integral involving the extension of Zeta-function, a general class of polynomials,the multivariable Aleph-function,the multivariable I-function and elliptic integral of the first kind

F.Y.Ayant

Abstract

In the present paper we evaluate a generalized finite integral involving the product of a extension of the Hurwitz-lerch Zeta-function,the complete elliptic integral, the multivariable Aleph-function, the multivariable I-function defined byPrasad 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 polynomial, extension of the Hurwitz-lerch Zeta-function, incomplete gamma function, multivariable I-function.

References

[1]Abramowitz M and Stegun I.A. Handbook of Mathematical Functions ,1964,
[2] Brychkow Y.A. Handbook of Special Functions. Derivatives. Integrals, Series and Other Formulas. CRC. Press. Taykor and Francis Group. Boca. Raton. London. New York. 2008.
[3] Y.N. Prasad , Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 ( 1986 ) , page 231-237.
[4] Sharma C.K.and Ahmad S.S.: On the multivariable I-function. Acta ciencia Indica Math , 1994 vol 20,no2, p 113- 116.
[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] 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.
[7] 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
[8] Whittaker E.T and Watson G.N. A course of modern analysis. Naw York. Mac Millan 1943.

Citation :

F.Y.Ayant, "Generalized finite integral involving the extension of Zeta-function, a general class of polynomials,the multivariable Aleph-function,the multivariable I-function and elliptic integral of the first kind," International Journal of Mathematics Trends and Technology (IJMTT), vol. 46, no. 3, pp. 150-158, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V46P524