coefficient in trigonometrics sums in Mathematica

Question

I would like to compute coefficient in mathematica. for example I wrote this code to find the coefficients of cos(kx) in (a+b*cos(x))^4 where "a" and "b" are parameters.

f[x_] := (a + b Cos[x])^4

f1[x_] := TrigReduce[f[x]]

g[x_, k_] := Coefficient[f1[x], Cos[k x]]

it works for the coefficients of cos(k*x),

for example the coefficient of cos(2x) is

g[x,2]= 1/8 (24 a^2 b^2 + 4 b^4)

but it does not work for constant(here constant means independent of cos(kx). In other words, just the terms with numbers and the parameters "a" and "b").

I would like to write the code to find the constant in the above meaning.

thanks.

Answer 1

Plugging Coefficient[TrigReduce[(a + b*Cos[x])^4],Cos[2*x]] into Wolfram|Alpha produced the output you wanted it to. This leads me to suggest that your problem might have to do with how the expression is being evaluated as opposed to a problem with how you are mathematically thinking about it.

I do not have access to a copy of Mathematica so can not test this, but I would try changing := to = in the second line of code.

I would also try putting it all in one line as

g[x_, k_] := Coefficient[TrigReduce[(a + b Cos[x])^4], Cos[k x]]

If that works, it is definitely something wrong with how/when Mathematica is assigning stuff.

See this link for more information.