Integral involving a generalized multiple-index Mittag-Leffler function,hyperbolic functions, a class of polynomials multivariable Aleph-function and multivariable I-function I

  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-V53P515

MLA

F.Y.Ayant "Integral involving a generalized multiple-index Mittag-Leffler function,hyperbolic functions, a class of polynomials multivariable Aleph-function and multivariable I-function I", International Journal of Mathematics Trends and Technology (IJMTT). V53(2):126-136 January 2018. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
In the present paper we evaluate a general integral involving the product of a generalized multiple-index Mittag-Leffler function,hyperbolic functions, multivariable Aleph-function, the multivariable I-function defined by Prasad [4] 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.

Reference
[1]Gradshteyn I.S and Ryzhik I.N. Tables of integrals, series and products, Fourth ed. Academic. Press. New York (1980).
[2] J. Paneva-Konovska, Multi-index (3m-parametric) Mittag-Leffler functions and fractional calculus.Compt. Rend. de l’Acad. Bulgare des Sci. 64, No 8 (2011), page 1089–1098.
[3] T. R. Prabhakar, A singular integral equation with a generalizedMittag-Leffler function in the kernel.Yokohama Math. J.19(1971), page 7–15.
[4] Y.N. Prasad , Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 ( 1986 ) , page 231-237.
[5] Sharma C.K.and Ahmad S.S.: On the multivariable I-function. Acta ciencia Indica Math , 1994 vol 20,no2, p 113- 116.
[6] 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.
[7] 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 Aleph-function, general class of polynomials, generalized multiple-index Mittag-Leffler function, multivariable I-function, multivariable H-function.