On the Fourier coefficients of the derivative with respect to celebrated orthogonal systems
Year: 2024
Type: article
Abstract: The main goal of this paper is to find the coefficients of the Jacobi polynomials and the integrals of Legendre polynomials expansion of the derivative of a function in terms of the coefficients in the expansion of the original function. More precisely, if {Q_{n}} is a sequence or orthogonal polynomials, and if p(x)=∑_{j=0}ⁿa_{j}Q_{n-j}(x) is such that p′(x)=∑_{j=0}ⁿ⁻¹d_{j}Q_{n-j-1}(x), we find an explicit relation for the coefficients d_{j}, as linear combinations of the coefficients a_{j}. This will be done for two celebrated classes of orthogonal functions, namely the Jacobi polynomials and the integrals of the Legendre polynomials.
Author: Abdelhamid Rehouma
Institution: University of Eloued
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4395674747