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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 37 | Number 2 | Year 2016 | Article Id. IJMTT-V37P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V37P515

Eulerian integrals involving the multivariable I-function I


F.Y.Ayant
Abstract

In this paper, we derive a general Eulerian integral involving the multivariable I-function defined by Prasad [3], the Aleph-function of one variable, a general class of polynomials of several variables and a extension of the Hurwitz-lerch Zeta-function. Some of this key formula could provide useful generalizations of some known as well as of some new results concerning the multivariable H-function.

Keywords
Eulerian integral, Multivariable I-function, general class of polynomial, Aleph-function, multivariable H-function, a extension of the Hurwitz-lerch Zeta-function.
References

[1]Appell P. and Kampe de Feriet J. Fonctions hypergeometriques et hypersphériques, polynôme d'Hermite, Gautier- Vilars. Paris (1926).
[2] Chaurasia V.B.L and Singh Y. New generalization of integral equations of fredholm type using Aleph-function Int. J. of Modern Math. Sci. 9(3), 2014, p 208-220.
[3] Y.N. Prasad , Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 ( 1986 ) , page 231-237.
[4] 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.
[5] H.M. Srivastava and Hussain M.A. Fractional integration of the H-function of several variables. Comp. Math. Appl. 30(9), (1995), page 73-85.
[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] Südland N.; Baumann, B. and Nonnenmacher T.F. , Open problem : who knows about the Aleph-functions? Fract. Calc. Appl. Anal., 1(4) (1998): 401-402.

Citation :

F.Y.Ayant, "Eulerian integrals involving the multivariable I-function I," International Journal of Mathematics Trends and Technology (IJMTT), vol. 37, no. 2, pp. 102-111, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V37P515

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