On a unified integral formula involving multivariable A-functions and classes of polynomials

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2018 by IJMTT Journal
Volume-53 Number-2
Year of Publication : 2018
Authors : F.Y.Ayant
  10.14445/22315373/IJMTT-V53P519

MLA

F.Y.Ayant "On a unified integral formula involving multivariable A-functions and classes of polynomials", International Journal of Mathematics Trends and Technology (IJMTT). V53(2):158-165 January 2018. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
In this paper we evaluate a unified and general finite integral involves the product of the multivariable A-functions defined by Gautam et al [1] and the general classes of multivariable polynomials with general arguments. On account of the most general nature of the functions and the classes of the polynomials and their general arguments occuring in our main integral, several new and known integrals follow as its simple specials cases. We shall study the particular case concerning the multivariable H-function defined by Srivastava et al [6] and the Srivastava-Daoust polynomial [3].

Reference
[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] Srivastava H.M., Gupta K.C. and Goyal S.P. The H-functions of one and two variables with applications. South Asian Publishers, New Delhi, Madras, 1982.
[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.

Keywords
Multivariable A-function, general class of multivariable polynomials, multivariable H-function.