N. H. Bingham, Tasmin L. Symons
Published 2021-01-28Version 1
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.
Comments: The results in this paper replace Section 4 in arXiv:1812.02103v1
A $(p,ν)$-extension of the Appell function $F_1(\cdot)$ and its properties
Integral representation of some functions related to the Gamma function
Two forms of the integral representations of the Mittag-Leffler function
![QR code for arXiv:2101.11809 [math.CA]](http://oss.arxitics.com/images/favicon.svg)