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

Frédéric Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V39P525

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 39 | Number 3 | Year 2016 | Article Id. IJMTT-V39P525 | DOI : https://doi.org/10.14445/22315373/IJMTT-V39P525

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

Frédéric Ayant

Citation :

Frédéric Ayant, "Fourier expansion of generalized prolate spheroidal wave function concerning generalized polynomials ,Aleph-function and multivariable I-function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 39, no. 3, pp. 206-214, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V39P525

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 I-function. This integral formula has been employed to obtain an expansion formula for multivariable I-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 I-function, Aleph-function, class of multivariable polynomials, generalized hypergeometric function, finite integral, generalized prolate spheroidal wave function, expansion formula, multivariable H-function.

References

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