直交関数列
1と余弦関数による列{1, cosx, cos2x, cos3x,...}は区間 [0, π] で直交関数系を成す。
∫ 0 π 1 d x = π {\displaystyle \int _{0}^{\pi }1\,dx=\pi }
∫ 0 π 1 ⋅ cos  n x d x = 0 ( n = 1 , 2 , ... ) {\displaystyle \int _{0}^{\pi }1\cdot \cos {nx}\,dx=0\quad (n=1,2,\dots )}
∫ 0 π cos  m x ⋅ cos  n x d x = π 2 δ m n ( m , n = 1 , 2 , ... ) {\displaystyle \int _{0}^{\pi }\cos {mx}\cdot \cos {nx}\,dx={\frac {\pi }{2}}\delta _{mn}\quad (m,n=1,2,\dots )}