A note on dual integral equations involving associated Legendre function
type: Item
instance of: scholarly article
title: A note on dual integral equations involving associated Legendre function
zbMATH Open document ID: 0755.45004
DOI: 10.1155/S0161171292000760
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/46741
review text: The author obtains a closed form solution of the following dual integral equations: \[ \int^ \infty_ 0\sigma^{-1}A(\sigma)P^ \mu_{- 1/2+i\sigma}(\cosh\alpha)\tanh c\sigma d\sigma=f(\alpha),\quad 0<\alphaa, \tag{2} \] with \(\text{Re} \mu<1/2\). He first finds a closed form solution of the pair of dual integral equations consisting of (1) and (2) with \(g(\alpha)=0\) and then the solution of the pair consisting of (1) with \(f(\alpha)=0\) and (2). The desired solution of equations (1) and (2) is then obtained by combining solutions of these two pairs. The method used here is formal and no attempt is made to find precise conditions under which the solution obtained is valid.
Mathematics Subject Classification ID: 45F10
zbMATH DE Number: 89253
zbMATH Keywords: associated Legendre function
zbMATH Keywords: closed form solution
zbMATH Keywords: dual integral equations
author: B. N. Mandal
reviewed by: Som Prakash Goyal
MaRDI profile type: Publication
OpenAlex ID: W2085843970
description: scientific article; zbMATH DE number 89253