Unification of Ramanujan Integrals with Some Infinite Integrals and Multivariable Gimel-Function

Frédéric Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V60P521

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 60 | Number 3 | Year 2018 | Article Id. IJMTT-V60P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V60P521

Unification of Ramanujan Integrals with Some Infinite Integrals and Multivariable Gimel-Function

Frédéric Ayant

Abstract

In the present paper some Ramanujan integrals are unified with some infinite integrals and multivariable Gimel-function. The importance of our main results lies in the fact that they involve special functions and multivariable Gimel-function which are sufficiently general in nature and capable of yielding a large number or simpler and useful results merely by specializing the parameters therein.

Keywords

Multivariable Gimel-function, multiple integral contours, Ramanujan integrals, generalized hypergeometric function.

References

[1] R.P. Agarwal, Resonance of Ramanujan’s Mathematics, Vol I, New age International (P) Ltd, 1996.
[2] 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.
[3] B.C. Bernt; Ramanujan’s Notebook Pat I-V, Springer-Verlag, New York (1985, 1989, 1991, 1994, 1998).
[4] B.L.J. Braaksma, Asymptotics expansions and analytic continuations for a class of Barnes-integrals, Compositio Math. 15 (1962-1964), 239-341.
[5] V. Kumar and S. Nagar, Unification of Ramanujan integrals with some infinite integrals and multivariable Hfunction, Vijnana parishad Anusandhan patrika, 55(3) (2012), 27-32.
[6] Y.N. Prasad, Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 (1986) , 231-237.
[7] 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.
[8] 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.
[9] 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, "Unification of Ramanujan Integrals with Some Infinite Integrals and Multivariable Gimel-Function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 60, no. 3, pp. 133-141, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V60P521