...

  • Home
  • Articles
    • Current Issue
    • Archives
  • Authors
    • Author Guidelines
    • Policies
    • Downloads
  • Editors
  • Reviewers
...

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 36 | Number 1 | Year 2016 | Article Id. IJMTT-V36P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V36P501

Fourier expansion of generalized prolate spheroidal wave function concerning generalized polynomials ,Aleph-function and multivariable Aleph-function


F.Y . Ayant
Abstract

The object of the paper is to establish an integral formula involving the generalized prolate spheroidal wave function, generalized hypergeometric function, generalized polynomials, Aleph-function of one variable and multivariable Aleph-function. This integral formula has been employed to obtain an expansion formula for multivariable Aleph-function, generalized hypergeometric function, a class of polynomial and Aleph-function in terms of generalized prolate spheroidal wave function.This expansion formula being of very general nature can be transformed to provide many new results involving various commonly used special functions occuring in applied mathematics, mathematics physics and mchanics. During the course of finding, we establish several particular cases.

Keywords
generalized multivariable Aleph-function, Aleph-function, class of multivariable polynomials, generalized hypergeometric function, finite integral, generalized prolate spheroidal wave function, expansion formula.
References

[1] Ayant F.Y. An integral associated with the Aleph-functions of several variables. International Journal of Mathematics Trends and Technology (IJMTT). 2016 Vol 31 (3), page 142-154.
[2] Chaurasia V.B.L and Singh Y. New generalization of integral equations of fredholm type using Aleph-function Int. J. of Modern Math. Sci. 9(3), 2014, p 208-220.
[3] Erdelyi A. et al Tables of integral transforms,Vol II. Mc. Graw-Hill, New York (1954).
[4] Gupta R.K. Generalized prolate spheroidal wave functions. Proc. India. Acad. Sci 85A (2), (1977),page 104-114.
[5] Sharma C.K.and Ahmad S.S.: On the multivariable I-function. Acta ciencia Indica Math , 1994 vol 20,no2, p 113- 116.
[6] Sharma C.K. and Mishra P.L.: On the I-function of two variables and its properties. Acta Ciencia Indica Math , 1991, Vol 17 page 667-672.
[7] Sharma K. On the integral representation and applications of the generalized function of two variables , International Journal of Mathematical Engineering and Sciences , Vol 3 , issue1 ( 2014 ) , page1-13.
[8] Sharma S.D. Multiple generalized prolate spheroidal wave transforms and its applications . Kyungpook Mathematical Journal, Vol 20 (1) ,( 1980), page 121-127.
[9] Srivastava H.M. A multilinear generating function for the Konhauser set of biorthogonal polynomials suggested by Laguerre polynomial, Pacific. J. Math. 177(1985), page183-191.
[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.

Citation :

F.Y . Ayant, "Fourier expansion of generalized prolate spheroidal wave function concerning generalized polynomials ,Aleph-function and multivariable Aleph-function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 36, no. 1, pp. 1-10, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V36P501

  • PDF
  • Abstract
  • Keywords
  • References
  • Citation
Abstract Keywords References Citation
  • Home
  • Authors Guidelines
  • Paper Submission
  • APC
  • Archives
  • Downloads
  • Open Access
  • Publication Ethics
  • Copyrights Infringement
  • Journals
  • FAQ
  • Contact Us

Follow Us

Copyright © 2025 Seventh Sense Research Group® . All Rights Reserved