Integration of Certain Generalized Gimel-Function with Respect to their Parameters

Frédéric Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V56P526

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 56 | Number 3 | Year 2018 | Article Id. IJMTT-V56P526 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P526

Integration of Certain Generalized Gimel-Function with Respect to their Parameters

Frédéric Ayant

Abstract

The object of the present paper is to establish a new class of two-dimensional series expansion of generalized multivariable Gimel-function involving Bessel’s function.

Keywords

Generalized multivariable Gimel-function, multiple integral contours, Two-dimensional series, Bessel’s function, orthogonal property

References

[1] N. Agarwal, A. Goyal and R.D. Agarwal, New class of two dimensional series expansion for product of Bessel’s function and I-function of two variables.
[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.L.J. Braaksma, Asymptotics expansions and analytic continuations for a class of Barnes-integrals, Compositio Math. 15 (1962-1964), 239-341.
[4] A. Goyal and R.D. Agrawal, integral involving the product of I-function of two variables, Jour. M.A.C.T. 28(1995), 147-155.
[5] Y.L. Luke, Integrals of Bessel functions, McGraw Hill, New York (1962).
[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] E.D. Rainville, Special functions, Mac Millan and Co, New York (1960).
[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, "Integration of Certain Generalized Gimel-Function with Respect to their Parameters," International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 3, pp. 180-186, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P526