Integral Representations of Ultraspherical Polynomials II

Autor:	Bingham, N. H., Symons, Tasmin L.
Rok vydání:	2021
Předmět:	Mathematics - Classical Analysis and ODEs 42C05 33C45
Druh dokumentu:	Working Paper
Popis:	In the first part, by the first author's work of 1972, an integral representation for an ultraspherical polynomial of higher index in terms of one of lower index and an infinite series was obtained. While this representation works well from a theoretical point of view, it is not numerically satisfactory as it involves polynomials of high degree, which are numerically unstable. Here we sum this series to obtain an integral, which is numerically tractable. Comment: The results in this paper replace Section 4 in arXiv:1812.02103v1
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2101.11809 Zobrazit plný text záznamu View this record from Arxiv