General Infinite integral involving the sequence of functions, a class of polynomials and multivariable Aleph-functions I

International Journal of Mathematics Trends and Technology (IJMTT)
© 2016 by IJMTT Journal
Volume-36 Number-3
Year of Publication : 2016
Authors : F.Y.Ayant


F.Y.Ayant "General Infinite integral involving the sequence of functions, a class of polynomials and multivariable Aleph-functions I", International Journal of Mathematics Trends and Technology (IJMTT). V36(3)180-191 August 2016. ISSN:2231-5373. Published by Seventh Sense Research Group.

In the present paper we evaluate a generalized infinite integral involving the product of the sequence of functions, the multivariable Aleph-functions and general class of polynomials of several variables with general arguments. 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.

[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] Fujiwara I. A unified presentation of classical orthogonal polynomials. Math. Japon. 11 (1966), page133-148.
[3]Marichev O.I. Prudnikov A.P. And Brychkow Y.A. Elementay functions. Integrals and series Vol 1. USSR Academyof sciences . Moscow 1986.
[4] 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
[5] 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.
[6] Sharma C.K.and Ahmad S.S.: On the multivariable I-function. Acta ciencia Indica Math , 1994 vol 20,no2, p 113- 116.
[7] C.K. Sharma and P.L. mishra : On the I-function of two variables and its properties. Acta Ciencia Indica Math , 1991, Vol 17 page 667-672.
[8] Sharma K. On the integral representation and applications of the generalized function of two variables , International Journal of Mathematical Engineering and Sciences , Vol 3 , issue1 ( 2014 ) , page1-13.
[9] 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.

Multivariable Aleph-function, general class of polynomials, sequence of functions, multivariable I-function, Aleph-function of two variable, I-function of two variables.