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Re: Finding roots of equalities involving Legendre Polynomials

• To: mathgroup at smc.vnet.net
• Subject: [mg66790] Re: Finding roots of equalities involving Legendre Polynomials
• From: Jens Hueschelrath <nospam_jens at hueschelrath.de>
• Date: Tue, 30 May 2006 05:48:56 -0400 (EDT)
• References: <e3mip0$7d0$1@smc.vnet.net> <e3uojd$icf$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Paul Abbott wrote:
> In article <e3mip0$7d0$1 at smc.vnet.net>,
>  Jens Hueschelrath <nospam_jens at hueschelrath.de> wrote:

> Note that Mathematica can compute and simplify this derivative:
> 
>   der[q_,m_][theta_]= Simplify[D[LegendreP[q, -m, Cos[theta]], theta]]

Dear Paul,

your hints turned out to be very helpful to me, thank you very much for 
that! But there remains one problem that I was not yet able to solve.
The derivative, as you define it above works well as long it is 
performed on 'theta'.
Unfortunately, the expression I try to compute is also using derivatives 
with respect to 'q'.  I tried to evaluate

  Simplify[D[LegendreP[q,1,Cos[theta]],q] or
  Simplify[D[LegendreP[q,1,Cos[theta]],theta0, q]

in Mathematica, but without any success. The only idea I have on this is 
to use a series expansion of LegendreP and to differentiate this series...

best regards

	Jens