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