Integrals transforms and Fourier series containing some product os special functions

F.Y. Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V63P511

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 63 | Number 2 | Year 2018 | Article Id. IJMTT-V63P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V63P511

Integrals transforms and Fourier series containing some product os special functions

F.Y. Ayant

Abstract

In this paper, first we present three integrals pertaining to some special functions like Aleph-function, generalization of M-series, multivariable alephfunction and the general class of polynomials. Later, we give three Fourier series for the product of some special functions like Aleph-function, generalized M-series, multivariable aleph-function and the general class of polynomials which have been obtained by the application of the integrals derived in first time.

Keywords

Aleph-function, general polynomials, multivariable Aleph-function, integrals, Fourier series, generalization of M-series.

References

[1] F.Y. Ayant, A Fractional Integration of the Product of Two Multivariable Aleph-Functions and a General Class of Polynomials I, Int. Jr. of Mathematical Sciences & Applications, 7(2) (2017), 181-198.
[2] V.B.L. Chaurasia and Y. Singh, New generalization of integral equations of fredholm type using Aleph-function Int. J. of Modern Math. Sci. 9(3), 2014, p 208-220.
[3] D.B.D.E. Honn, Nouvelles integrales, Haipnar publishing (1957).
[4] T.Salim, A. Faraz, S. Sadek and J.Ismail, A generalized of M-serie and integral operator associated with fractional calculus, Asian Journal of Fuzzy and Applied Mathematics 2(5) (2014), 142-155,
[5] M. Sharma and R. Jain, A note on a generalized M-series as a special function, Fractional Calculus Applied Analysis, 12 (2009), 449-452.
[6] I.N. Sneddon, Special functions of Mathematical Physics and Chemistry, Oliver and Boyd, Edinburgh and London, New York, Inter Science Publication (1956).
[7] H.M. Srivastava, A contour integral involving Fox’s H-function, Indian. J. Math. 14(1972), 1-6.
[8] 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), page.119-137.
[9] H.M. Srivastava and R. Panda, Some expansion theorems and generating relations for the H-function of several complex variables II. Comment. Math. Univ. St. Paul. 25(1976), page.167-197.
[10] H.M. Srivastava and N.P. Singh, The integration of certains products of the multivariable H-function with a general class of polynomials, Rend. CirC. Mat. Palermo. 32(2)(1983), 157-187.
[11] 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.
[12] Südland N.; Baumann, B. and Nonnenmacher T.F, Fractional driftless Fokker-Planck equation with power law diffusion coefficients, in V.G. Gangha, E.W. Mayr, W.G. Vorozhtsov (Eds.), Computer Algebra in Scientific computing (CASC) Konstanz 2001), Springer, Berlin, (2001), 513-525.

Citation :

F.Y. Ayant, "Integrals transforms and Fourier series containing some product os special functions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 63, no. 2, pp. 82-88, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V63P511