On the expression for the product of any two Legendre's coefficients by means of a series of Legendre's coefficients.
type: Item
instance of: scholarly article
title: On the expression for the product of any two Legendre's coefficients by means of a series of Legendre's coefficients.
zbMATH Open document ID: 10.0337.01
author: John Couch Adams
published in: Proceedings of the Royal Society of London
publication date: 1878-01-01T00:00:00Z
review text: Der Verfasser hat früher (Febr. 1873) den Satz gefunden: \[ \int_{-1}^1P_mP_nP_pdp =\frac1{s+\frac12} \frac{A(s-m)A(s-n)A(s-p)}{A(s)}, \] wo \[ s=\frac12(m+n+p) \quad \text{und}\quad A(m)=2^m\cdot \frac{\frac12\cdot \frac32\cdot m-\frac12}{1\cdot2\cdots m} \] \[ =2^m\cdot \frac{\varPi(m-\frac12)}{\varPi(m)\varPi(-\frac12)}. \] Der Satz wurde unabhängig auch 1874 von Herrn Ferrers entdeckt und ist in seinen ``Spherical harmonics'' London 1877 publicirt.
Mathematics Subject Classification ID: 33C55
zbMATH DE Number: 2711221
zbMATH Keywords: spherical harmonics
MaRDI profile type: Publication
full work available at URL: rspl.1878.0016
OpenAlex ID: W2029238974
Wikidata QID: Q110504961
DOI: 10.1098/RSPL.1878.0016
description: scientific article; zbMATH DE number 2711221