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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 39 | Number 2 | Year 2016 | Article Id. IJMTT-V39P520 | DOI : https://doi.org/10.14445/22315373/IJMTT-V39P520

Certain finite double integrals involving biorthogonal polynomial, a general class of polynomials and multivariable I-function


Frédéric Ayant
Abstract

In this paper, we evaluate three finite double integrals involving varous products of biorthogonal polynomials, a general class of polynomial and multivariable I-function with general arguments. The integrals evaluated are quite general in nature and yield a number of new integrals as special cases.

Keywords
I-function of several variables, finite double integral, H-function of several variables , general class of polynomials.
References

[1] Chai W.A., Carlitz L. Biorthogonal condition for a class of polynomials, SIAM. Rev. 14 (1972), 494; ibid 15(1973), p. 670-672.
[2] Erdelyi A. et al Higher transcendental functions, Vol1 McGraw Hill, New York. (1953).
[3] Mac Robert T.M. Beta function formula and integrals involving E-functions, Math Ann, 142 (1961), p.450-452.
[4] Mathai A.M. And Saxena R.K. Generalized hypergeometric functions with applications in statistics and physical sciences. Lecture notes in Mathematics, Vol. 348, Springer Verlag, New York. (1973).
[5] Y.N. Prasad , Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 ( 1986 ) , page 231-237.
[6] Srivastava H.M. A multilinear generating function for the Konhauser set of biorthogonal polynomials suggested by Laguerre polynomial, Pacific. J. Math. Vol 77(1985), page183-191.
[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), p.119-137.

Citation :

Frédéric Ayant, "Certain finite double integrals involving biorthogonal polynomial, a general class of polynomials and multivariable I-function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 39, no. 2, pp. 165-173, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V39P520

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