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.

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]])

```

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