将 Euler- Fourier公式 f(tcos nt dt, b f(tsin nt da 代入Sn(x), S(x)= 7/J(l+(cos nt cos nx+ sinn sinx)dr f(o+>cosn(t-x)di将 Euler-Fourier 公式 an = π π 1 ( )cos d π f t nt t  − ，bn = π π 1 ( )sin d π f t nt t  − 代入S x m ( )， S x m ( ) π π 1 ( )d 2π f t t − =  ( ) ( ) π π π π 1 1 ( )cos d cos ( )sin d sin π m n f t nt t nx f t nt t nx − − =   + +        π π 1 1 1 ( ) (cos cos sin sin ) d π 2 m n f t nt nx nt nx t − =   = + +       π π 1 1 1 ( ) cos ( ) d π 2 m n f t n t x t − =   = + −      