Double Integrals Involving Multivariable Gimel-Function, General Class of Polynomials and Biorthogonal Polynomial

Frédéric Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V60P525

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 60 | Number 3 | Year 2018 | Article Id. IJMTT-V60P525 | DOI : https://doi.org/10.14445/22315373/IJMTT-V60P525

Double Integrals Involving Multivariable Gimel-Function, General Class of Polynomials and Biorthogonal Polynomial

Frédéric Ayant

Abstract

In the present paper, we evaluate a finite double integrals involving product of multivariable Gimel-function, biorthogonal polynomial and general class of polynomials. The integral evaluated is quite general in nature and yields a number of new integrals and its special cases.

Keywords

Multivariable Gimel-function, multiple integral contours, finite double integral, general class of polynomials, biorthogonal polynomials.

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] W.A. Chai and L. Carlitz, Biorthogonal conditions for a class of polynomials, SIAM, Rev, 14(1972), 494; ibid. 15 (1973), 670-672.
[4] R. Khan, Double integrals involving multivariable I-function, general class pf polynomials and biorthogonal polynomial. Vijnana Parishad Anusandhan Patrika, 56(4) (2013).
[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] H.M. Srivastava, A contour integral involving Fox’s H-function, Indian. J. Math. 14(1972), 1-6.
[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.
[10] H.M. Srivastava and N.P. Singh, The integration of certains products of the multivariable H-function with a general class of polynomials, Rend. CirC. Mat. Palermo. 32(2)(1983), 157-187.

Citation :

Frédéric Ayant, "Double Integrals Involving Multivariable Gimel-Function, General Class of Polynomials and Biorthogonal Polynomial," International Journal of Mathematics Trends and Technology (IJMTT), vol. 60, no. 3, pp. 161-167, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V60P525