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