Numerical evaluation of the \(p\)th derivative of Jacobi series
An algorithm for the evaluation of the \(p\)th derivative at a given point of a polynomial expressed as a finite series of Jacobi polynomials is established. The algorithm permits the direct evaluation without obtaining the \(p\)th derivative of the polynomial itself, resulting in memory and time savings. Another algorithm for reducing the rounding errors near the end points of the interal of evaluation is given. The results established can be applied to various particular cases of Jacobi polynomials such as ultraspherical, Legendre and Chebyshev polynomials.
scientific article; zbMATH DE number 1879034
scientific article