Finding roots of equalities involving Legendre Polynomials

*To*: mathgroup at smc.vnet.net*Subject*: [mg66287] Finding roots of equalities involving Legendre Polynomials*From*: Jens Hueschelrath <nospam_jens at hueschelrath.de>*Date*: Mon, 8 May 2006 00:46:02 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Dear all, in order to solve an electromagnetic scattering problem, I try to find the positive roots of two equalities: LegendreP[p, -m, Cos[theta1]] == 0 theta1 is known and m = 0,1,2,... as well as D[LegendreP[q,-m, Cos[theta1]], theta1] == 0 with, again, theta1 known and m = 0,1,2,... The values of p and q are needed for series expressions like : E = Sum_{p}[....] + Sum_{q}[....] where p and q are all the positive roots of the equations from above. Up to now I was unable to solve this problem with my Mathematica 5.2... Any ideas on this? Thanks a lot in advance! Jens