A unified study of Fourier series involving the Aleph-function and the Kampé de Fériet's function

Frédéric Ayant; Dinesh Kumar

doi:https://doi.org/10.14445/22315373/IJMTT-V35P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 35 | Number 1 | Year 2016 | Article Id. IJMTT-V35P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V35P507

A unified study of Fourier series involving the Aleph-function and the Kampé de Fériet's function

Frédéric Ayant, Dinesh Kumar

Abstract

Recently Yashwant Singh et al [7] have studied Fourier series involving the I-function defined by V.P. Saxena [6]. Motivated by this work, we make an application of an integral involving sine function, exponential function, the product of Aleph-function of one variable and Kampé de Fériet's function. We also evaluate a multiple integral involving the Aleph-function to make its application to derive a multiple exponential Fourier series. Several particular cases are also given at the end.

Keywords

Fourier series , Aleph-function , Kampé de Fériet's function

References

[1] Appel P. and Kampé de Fériet J. Fonctions hypergéométriques et hyperspheriques ; Polynômes D'hermite , Gauthier-Villars , Paris . 1926
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[3] Mishra S. Integrals involving Legendre functions,generalized hypergeometric series and Fox’s H-function , and Fourier-Legendre series for products of generalized hypergeometric functions, Indian J. Pure Appl.Math., 21(1990), page 805-812.
[4] Ram J. and Kumar D.; Generalized fractional integration of the Aleph-function, J. Raj. Acad. Phy. Sci., Vol. 10, No. 4, December (2011), page 373-382.
[5] Saxena R.K. and Kumar D. ; Generalized fractional calculus of the Aleph-function involving a general class of polynomials , Acta Mathematica Scientia , Volume 35, Issue 5, September 2015, page 1095–1110, (2015).
[6] Saxena V.P. Formal solution of certain new pair of dual integral equations involving H-function, Proc. Nat. Acad. Sci. India, A52, (1982), page 366-375.
[7] Singh Y. and Khan N.A. A unified study of Fourier series involving generalized hypergeometric function. Global journal of science frontier research:G.J.S.F.R. (F) vol 12(4) (2012) , page 44-55
[8] Südland N.; Baumann, B. and Nonnenmacher T.F. , Open problem : who knows about the Aleph-functions? Fract. Calc. Appl. Anal., 1(4) (1998), page 401-402.

Citation :

Frédéric Ayant, Dinesh Kumar, "A unified study of Fourier series involving the Aleph-function and the Kampé de Fériet's function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 35, no. 1, pp. 40-48, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V35P507