A General Multiple Eulerian Integrals Involving General Classes of Polynomials, A Multivariable I-Function and The Generalized Incomplete Hypergeometric Function

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2018 by IJMTT Journal
Volume-54 Number-1
Year of Publication : 2018
Authors : F.Y.Ayant
  10.14445/22315373/IJMTT-V54P503

MLA

F.Y.Ayant "A General Multiple Eulerian Integrals Involving General Classes of Polynomials, A Multivariable I-Function and The Generalized Incomplete Hypergeometric Function ", International Journal of Mathematics Trends and Technology (IJMTT). V54(1):24-33 February 2018. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
Recently, Goyal and Parashar [2] have given cloosed-form expression for a number of general Eulerian integrals involving multivariable H-function. The object of the present papers is to evaluate a general class of multiple Eulerian integral involving the product of a general class of multivariable polynomials, the generalized incomplete hypergeometric function and the multivariable I-function defined by Nambisan et al [4]. with general arguments. This integral formula provides interesting unifications and extensions of a number of (know and new) integrals. Several particular cases will study.

Reference
[1] B. L. J. Braaksma, “Asymptotic expansions and analytic continuations for a class of Barnes integrals,”Compositio Mathematical, vol. 15, pp. 239–341, 1964.
[2] Goyal S.P. And Parashad A. A multiple Eulerian integral. Far East J. Math. Sci 1(6) (1999), page 1003-1013.
[3] Gradshteyn I.S. and Ryxhik I.M. Table of integrals, series and products. Academic Press, NewYork, 1980
[4] 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
[5] Srivastava H.M. Chaudhry M.A and Agarwal R.P. The incomplete Pochhammer symbols and their in applications to hypergeometric and related functions. Integral Transforms ans Special Functions 23 (2012), page 659-683.
[6] 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.
[7] Srivastava H.M. And Garg M. Some integral involving a general class of polynomials and multivariable Hfunction. Rev. Roumaine Phys. 32(1987), page 685-692.
[8] H.M. Srivastava And R.Panda. Some expansion theorems and generat

Keywords
Multivariable I-function, multiple Eulerian integral , multivariable H-function, Srivastava-Daoust polynomial, generalized incomplete hypergeometric function