Integrals and Fourier series involving the product of biorthogonal polynomials and special functions

F.Y. Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V63P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 63 | Number 1 | Year 2018 | Article Id. IJMTT-V63P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V63P509

Integrals and Fourier series involving the product of biorthogonal polynomials and special functions

F.Y. Ayant

Citation :

F.Y. Ayant, "Integrals and Fourier series involving the product of biorthogonal polynomials and special functions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 63, no. 1, pp. 68-74, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V63P509

Abstract

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

Keywords

Aleph-function, general polynomials, multivariable Aleph-function, integrals, biorthogonal polynomials, Fourier series, 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] T.R. Prabhakar and R.C. Tomar, Some integrals and series relations for biorthogonal polynomials suggested by the Legendre polynomials, Ind. Journal pure applied Mathematics 11(7) (1980), 863-869.
[4] M. Sharma and R. Jain, A note on a generalized M-series as a special function, Fractional Calculus Applied Analysis, 12 (2009), 449-452.
[5] H.M. Srivastava, A contour integral involving Fox’s H-function, Indian. J. Math. 14(1972), 1-6.
[6] H.M. Srivastava, A multilinear generating function for the Konhauser set of biorthogonal polynomials suggested by Laguerre polynomial, Pacific. J. Math. 177(1985), 183-191.
[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), page.119-137.
[8] ] 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.
[9] 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.
[10] 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.