Extract coefficients of a trig polynomial
- To: mathgroup at smc.vnet.net
- Subject: [mg126121] Extract coefficients of a trig polynomial
- From: Sam Takoy <sam.takoy at yahoo.com>
- Date: Thu, 19 Apr 2012 03:54:24 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
Hi, Suppose I have an expression that is a trigonometric polynomial in theta. Is there a way to neatly pick out the coefficients of the polynomial. I find that FourierCoefficient takes quite a bit of time, probably because it does a lot of integrations. My coefficients are very complicated expressions but do not depend on theta. Many thanks in advance, Sam PS: expr = (1/1536)(1536 BesselJ[0,\[Rho]]-72 \[Epsilon]^2 \[Rho]^2 BesselJ[0,\[Rho]]-80 \[Epsilon]^3 \[Rho]^2 BesselJ[0,\[Rho]]-384 \ [Epsilon] \[Rho] BesselJ[1,\[Rho]]-144 \[Epsilon]^2 \[Rho] BesselJ[1,\ [Rho]]-80 \[Epsilon]^3 \[Rho] BesselJ[1,\[Rho]]+10 \[Epsilon]^3 \ [Rho]^3 BesselJ[1,\[Rho]]-96 \[Epsilon]^2 \[Rho]^2 BesselJ[0,\[Rho]] Cos[2 \[Theta]]-120 \[Epsilon]^3 \[Rho]^2 BesselJ[0,\[Rho]] Cos[2 \ [Theta]]-384 \[Epsilon] \[Rho] BesselJ[1,\[Rho]] Cos[2 \[Theta]]-192 \ [Epsilon]^2 \[Rho] BesselJ[1,\[Rho]] Cos[2 \[Theta]]-120 \[Epsilon]^3 \ [Rho] BesselJ[1,\[Rho]] Cos[2 \[Theta]]+15 \[Epsilon]^3 \[Rho]^3 BesselJ[1,\[Rho]] Cos[2 \[Theta]]-24 \[Epsilon]^2 \[Rho]^2 BesselJ[0,\ [Rho]] Cos[4 \[Theta]]-48 \[Epsilon]^3 \[Rho]^2 BesselJ[0,\[Rho]] Cos[4 \[Theta]]-48 \[Epsilon]^2 \[Rho] BesselJ[1,\[Rho]] Cos[4 \ [Theta]]-48 \[Epsilon]^3 \[Rho] BesselJ[1,\[Rho]] Cos[4 \[Theta]]+6 \ [Epsilon]^3 \[Rho]^3 BesselJ[1,\[Rho]] Cos[4 \[Theta]]-8 \[Epsilon]^3 \ [Rho]^2 BesselJ[0,\[Rho]] Cos[6 \[Theta]]-8 \[Epsilon]^3 \[Rho] BesselJ[1,\[Rho]] Cos[6 \[Theta]]+\[Epsilon]^3 \[Rho]^3 BesselJ[1,\ [Rho]] Cos[6 \[Theta]])
- Follow-Ups:
- Re: Extract coefficients of a trig polynomial
- From: Barrie Stokes <Barrie.Stokes@newcastle.edu.au>
- Re: Extract coefficients of a trig polynomial
- From: Bob Hanlon <hanlonr357@gmail.com>
- Re: Extract coefficients of a trig polynomial