On integration of certain products involving general polynomials, Aleph-function and the multivariable Aleph-function

F.Y.Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V63P517

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 63 | Number 2 | Year 2018 | Article Id. IJMTT-V63P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V63P517

On integration of certain products involving general polynomials, Aleph-function and the multivariable Aleph-function

F.Y.Ayant

Abstract

The integrals evaluated here involve the product of Jacobi polynomials, Aleph-function, general polynomials and the multivariable Aleph-function. The main results of this paper are quite general in nature and capable of yielding a very large number of integrals involving polynomials and various special function occurring in the problems of mathematical analysis and mathematical physics.

Keywords

Jacobi polynomials, Aleph-function, general polynomials, multivariable Aleph-function, integrals.

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] B. Brafman, Generating function of Jacobi and related polynomials, Proc. Amer. Math. Soc. 2 (1951), 942-949.
[3] V.B.L. Chaurasia and R. Patni, On integration of certain products involving general polynomials, Fox’s H-function and the multivariable H-function, Jnanabha 28(1998), 63-70.
[4] 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.
[5] A. Erdélyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher Transcendental functions, Vol. 2, McGraw-Hill, New York, 1953.
[6] H.M. Srivastava, A contour integral involving Fox’s H-function, Indian. J. Math. 14(1972), 1-6.
[7] 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.
[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] 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.
[11] 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, "On integration of certain products involving general polynomials, Aleph-function and the multivariable Aleph-function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 63, no. 2, pp. 133-139, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V63P517