Certain Class of Eulerian Integrals of Multivariable Gimel-Function

Frédéric Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V59P520

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 59 | Number 2 | Year 2018 | Article Id. IJMTT-V59P520 | DOI : https://doi.org/10.14445/22315373/IJMTT-V59P520

Certain Class of Eulerian Integrals of Multivariable Gimel-Function

Frédéric Ayant

Abstract

In this present paper we evaluate a general class of Eulerian integrals involving the generalized multivariable Gimel-function. . The results proved here provide closes-form expression for numerous other potentially useful integrals. At the end , we shall establish several particular cases.

Keywords

Generalized multivariable Gimel-function, multiple integral contours, Eulerian integral.

References

[1] F. Ayant, An integral associated with the Aleph-functions of several variables. International Journal of Mathematics Trends and Technology (IJMTT), 31(3) (2016), 142-154.
[2] B.L.J. Braaksma, Asymptotics expansions and analytic continuations for a class of Barnes-integrals, Compositio Math. 15 (1962-1964), 239-341.
[3] A. Erdelyi, W. Magnus, F. Oberrhettinge and F.G. Tricomi, . Tables of integral transforms Vol I and II, McGraw-Hill, New York (1954).
[4] I.S. Gradshteyn and I.M. Ryzhik, Tables of integrals, series and products, academic New York, (1980).
[5] Y.N. Prasad, Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 (1986) , 231-237.
[6] J. Prathima, V. Nambisan and S.K. Kurumujji, A Study of I-function of Several Complex Variables, International Journal of Engineering Mathematics Vol (2014), 1-12.
[7] A.P. Prudnikov, Y.A. Brychkov and O.I Marichev, Integrals and series of elementary functions (in Russian), Nauka, Moscow (1981).
[8] H.S.P. Shrivastava, Certain class of Eulerian integrals of multivariable generalized hypergeometric function, J. Indian Acad. Math. 21(2) (1999), 2555-270.
[9] 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),119-137.
[10] H.M. Srivastava and R. Panda, Some expansion theorems and generating relations for the H-function of several complex variables II. Comment. Math. Univ. St. Paul. 25 (1976), 167-197.

Citation :

Frédéric Ayant, "Certain Class of Eulerian Integrals of Multivariable Gimel-Function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 59, no. 2, pp. 129-136, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V59P520