Services & ResourcesWolfram ForumsMathGroup Archive

[Date Index] [Thread Index] [Author Index]

Re: Extract coefficients of a trig polynomial

• To: mathgroup at smc.vnet.net
• Subject: [mg126124] Re: Extract coefficients of a trig polynomial
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Fri, 20 Apr 2012 07:42:11 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201204190754.DAA04272@smc.vnet.net>

coef = Module[{x}, Simplify[CoefficientList[
     expr /. Cos[n_. * \[Theta]] -> x^n, x]]]


Bob Hanlon


2012/4/19 Sam Takoy <sam.takoy at yahoo.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]])
>

• References:
  • Extract coefficients of a trig polynomial
    • From: Sam Takoy <sam.takoy@yahoo.com>