A representation of Jacobi functions
type: Item
instance of: scholarly article
title: A representation of Jacobi functions
zbMATH Open document ID: 0592.33011
DOI: 10.1155/S0161171285000795
author: E. L. Koh
author: Elias Y. Deeba
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46059
review text: Authors obtain an interesting series representation of Jacobi functions \[ P_{\lambda}^{(\alpha,\beta)}(x),\quad -\leq \alpha,\beta \leq,\quad \alpha +\beta =0,\quad and\quad \lambda \geq -. \] The continuous Jacobi transform and its inverse are used to obtain the result. When \(\lambda\) is a positive integer, the series representation reduces to a single term, that is, the Jacobi polynomial of degree n. The special case corresponding to \(\alpha =\beta =0\) is also examined. This paper represents an original contribution to the subject.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 3951000
zbMATH Keywords: Legendre functions
zbMATH Keywords: Jacobi functions
zbMATH Keywords: continuous Jacobi transform
zbMATH Keywords: Jacobi polynomial
reviewed by: Lokenath Debnath
MaRDI profile type: Publication
OpenAlex ID: W2137075786
description: scientific article; zbMATH DE number 3951000