把(sinx)^4展开成傅里叶级数,求过程

2025-12-13 04:23:07
推荐回答(1个)
回答1:

(sinx)^4 = (1/4)[2(sinx)^2]^2 = (1/4)(1-cos2x)^2
= (1/4)[1-2cos2x+(cos2x)^2]
= (1/4)(1-2cos2x + 1/2+(1/2)cos4x)
= (1/8)(3-4cos2x+cos4x)
然后套用 cos2x, cos4x 的傅里叶级数展开公式即得。