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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 35 | Number 1 | Year 2016 | Article Id. IJMTT-V35P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V35P508

Certain finite double integrals involving the hypergeometric function and Aleph-function


Frédéric Ayant, Dinesh Kumar
Abstract

The aim of this document is to evaluate four finite double integrals involving the product of two hypergeometric functions and the Alephfunction. At the end of this paper , we evaluate few particular cases

Keywords
Double finite integral , hypergeometric function , Aleph-function.
References

[1] Choi J. and Kumar D . ; Certain unified fractional integrals and derivatives for a product of Aleph function and a general class of multivariable polynomials, Journal of Inequalities and Applications, Vol. 2014 (2014), 15 pages.
[2] Fox's C. The G-function and H-function as symetric Fourier Kernels, Trans. Amer. Math. Soc. 98, (1961) page 396_429.
[3] Kumar D., Saxena R.K. and Ram J. : Finite Integral Formulas Involving Aleph Function , To appear ,16 pages
[4] Ronghe A.K.: Double integrals involving H-function of one variable , Vij. Pari. Anu. Patri 28(1) , (1985) page 33-38.
[5] Saxena R.K. , Ram J. and Kumar D. ; Generalized Fractional Integration of the Product of two Aleph -Functions Associated with the Appell Function 3 F , ROMAI , Journal, Vol.9, No.1 (2013), pp. 147-158.
[6] Saxena, V.P. Formal solution of certain new pair of dual integral equations involving H-function, Proc. Nat. Acad. Sci. India, A52, (1982), 366-275.
[7] G.Sharma and A.K. Rathie : Integrals of hypergeometric series , Vij. Pari. Anu. Patri 34(1-2) , (1991) page 26-29.
[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.

Citation :

Frédéric Ayant, Dinesh Kumar, "Certain finite double integrals involving the hypergeometric function and Aleph-function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 35, no. 1, pp. 49-55, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V35P508

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