چندجمله‌ای‌های متعامد

${\displaystyle ⟨f,g⟩={\int }_{x_1}^{x_2}f(x)g(x)dx.}$

${\displaystyle P_0(x)=1,}$

${\displaystyle P_1(x)=x,}$

${\displaystyle P_2(x)=\frac{3x^2-1}{2},}$

${\displaystyle P_3(x)=\frac{5x^3-3x}{2},}$

${\displaystyle P_4(x)=\frac{35x^4-30x^2+3}{8},}$

${\displaystyle ⋮}$

${\displaystyle {\int }_{-1}^1{P}_m(x)P_n(x)dx=0.}$