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MathGroup Archive 2006

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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


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