On general Eulerian integral of certain products of I-functions defined by Nambisan and a multivariable Aleph-function

F.Y. Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V42P518

International Journal of Mathematics Trends and Technology

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Volume 42 | Number 2 | Year 2017 | Article Id. IJMTT-V42P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V42P518

On general Eulerian integral of certain products of I-functions defined by Nambisan and a multivariable Aleph-function

F.Y. Ayant

Abstract

The object of this paper is to establish an general Eulerian integral involving the product of two multivariable I-functions defined by Nambisan et al [2], the expansion of multivariable Aleph-function and a generalized hypergeometric function which provide unification and extension of numerous results. We will study the particular case concerning the multivariable H-function.

Keywords

Eulerian integral, multivariable I-function, Lauricella function of several variables, multivariable H-function, generalized hypergeometric function

References

[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] 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
[3] Saigo M. and Saxena R.K. Unified fractional integral formulas for the multivariable H-function I. J.Fractional Calculus 15 (1999), page 91-107.
[4] Sharma C.K.and Ahmad S.S.: On the multivariable I-function. Acta ciencia Indica Math , 1994 vol 20,no2, p 113- 116.
[5] Srivastava H.M. and Karlsson P.W. Multiple Gaussian Hypergeometric series. Ellis.Horwood. Limited. New-York, Chichester. Brisbane. Toronto , 1985.
[6] Srivastava H.M. and Manocha H.L : A treatise of generating functions. Ellis. Horwood.Series. Mathematics and Applications 1984, page 60.
[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.

Citation :

F.Y. Ayant, "On general Eulerian integral of certain products of I-functions defined by Nambisan and a multivariable Aleph-function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 42, no. 2, pp. 147-158, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V42P518