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

Frédéric Ayant; Dinesh Kumar

doi:https://doi.org/10.14445/22315373/IJMTT-V35P508

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

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

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.