چندجمله‌ای‌های متعامد

${\displaystyle P_{0}(x)=1,\,}$

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

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

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

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

${\displaystyle \vdots }$

${\displaystyle \int _{-1}^{1}P_{m}(x)P_{n}(x)\,dx=0.}$