我想计算数学中的系数。例如，我编写了这段代码来查找 (a+b*cos(x))^4 中 cos(kx) 的系数，其中“a”和“b”是参数。
f[x_] := (a + b Cos[x])^4
f1[x_] := TrigReduce[f[x]]
g[x_, k_] := Coefficient[f1[x], Cos[k x]]
它适用于 cos(k*x) 的系数，
例如 cos(2x) 的系数是
g[x,2]= 1/8 (24 a^2 b^2 + 4 b^4)
但它不适用于常数（这里常数意味着独立于 cos(kx)。换句话说，只是带有数字和参数“a”和“b”的术语）。
我想编写代码来查找上述含义中的常量。
谢谢。
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.