A generalized formula for the integral of three associated Legendre polynomials
type: Item
instance of: scholarly article
title: A generalized formula for the integral of three associated Legendre polynomials
zbMATH Open document ID: 0942.33001
DOI: 10.1016/S0893-9659(98)00180-3
author: Yanyan Li
published in: Applied Mathematics Letters
publication date: 2000-04-09T00:00:00Z
review text: The authors present here a recurrence method for determining integrals \[ \int_{-1}^1 \prod_{k=1}^N P_{j_k}^{m_k} (z) dz,\qquad N=1,2,\dots, \] where the \[ P_j^m(z)= {1\over{\Gamma(1-m)}} \left( {z+1}\over{z-1}\right)^{m/2} \;_2F_1\Biggl[-j,j+1; 1-m; {{1-z}\over{2}} \Biggr] \] are associated Legendre polynomials. The application of the authors' method, with \(N=3\), for the flow over spheroids equations is also discussed.
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1369381
zbMATH Keywords: associated Legendre polynomials
reviewed by: Aleksey A. Dovgoshey
MaRDI profile type: Publication
cites work: ROTATORY AND LONGITUDINAL OSCILLATIONS OF AXI-SYMMETRIC BODIES IN A VISCOUS FLUID
cites work: The Stokes-flow drag on prolate and oblate spheroids during axial translatory accelerations
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cites work: Calculation of the steady flow past a sphere at low and moderate Reynolds numbers
full work available at URL: s0893-9659(98)00180-3
OpenAlex ID: W1974731904
description: scientific article; zbMATH DE number 1369381