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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 39 | Number 3 | Year 2016 | Article Id. IJMTT-V39P523 | DOI : https://doi.org/10.14445/22315373/IJMTT-V39P523

Some finite double integral involving general class of polynomials, special functions , Aleph-function and multivariable I-function


Frédéric Ayant
Abstract

The aim of the present document is to evaluate three triple double finite integrals involving general class of polynomials, special functions, Alephfunction and multivariable I-function. Importance of our findings lies in the fact that they involve the multivariable I-function, which are the sufficiently general in nature and are capable of yielding a large number of simpler and useful results merely by specializing the parameters in them. Further we establish some special cases.

Keywords
I-function of several variables, double integrals, special function, general class of polynomials, Aleph-function, multivariable Hfunction.
References

[1] Chaurasia V.B.L and Singh Y. New generalization of integral equations of fredholm type using the Aleph-function Int. J. of Modern Math. Sci. 9(3), 2014, p 208-220.
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[3] Erdelyi A. et al. Higher transcendental functions. , Vol 2, McGraw-Hill, New-York (1953).
[4] Mathai A.M. And Saxena R.K. (1973) : Generalized hypergeometric functions with applications in statistics and physical sciences, springer-Verlag, Lecture Notes No348, Heidelberg.
[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.
[8] Südland, N.; Baumann, B. and Nonnenmacher,T.F., Open problem : who knows about the Aleph-functions? Fract. Calc. Appl. Anal., 1(4) (1998): 401-402.
[9] Vyas V.M. and Rathie K., An integral involving hypergeometric function. The mathematics education 31(1997) page33

Citation :

Frédéric Ayant, "Some finite double integral involving general class of polynomials, special functions , Aleph-function and multivariable I-function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 39, no. 3, pp. 189-199, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V39P523

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