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

F.Y . Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V36P501

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

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

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

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