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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 57 | Number 3 | Year 2018 | Article Id. IJMTT-V57P529 | DOI : https://doi.org/10.14445/22315373/IJMTT-V57P529

Some Results Involving Generalized Multivariable Gimel-Function and Gegenbauer Polynomials


Frédéric Ayant
Abstract

In this paper an expension theorem for generalized multivariable Gimel-function has been obtained by using a series on Gegenbauer polynomials due to Askey [1]. This theorem is further utilized to evaluate an integral involving product of multivariable Gimel-function and Gegenbauer polynomials.

Keywords
Multivariable Gimel-function, multiple integral contours, Gegenbauer polynomials, expansion serie, finite integrals.
References

[1] R. Askey, Orthogonality expansions with positive coefficients, Proc. Amer. Math. Soc. 16(1965), 1191-1194.
[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] Y.N. Prasad, Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 (1986) , 231-237.
[5] 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.
[6] E.D. Rainville, Special functions, MacMillan and Co, New York, 1960.
[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),119-137.
[8] 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, "Some Results Involving Generalized Multivariable Gimel-Function and Gegenbauer Polynomials," International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 3, pp. 209-216, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P529

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