Re: Extract coefficients of a trig polynomial
- To: mathgroup at smc.vnet.net
- Subject: [mg126141] Re: Extract coefficients of a trig polynomial
- From: Ray Koopman <koopman at sfu.ca>
- Date: Fri, 20 Apr 2012 07:48:04 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <jmoge7$46g$1@smc.vnet.net>
On Apr 19, 12:55 am, Sam Takoy <sam.ta... at yahoo.com> wrote:
> 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]])
CoefficientList[ TrigExpand[expr], {Cos[=E8], Sin[=E8]} ]