Gegenbauer polynomial
= Gegenbauer polynomial
{c}
{title2=$C_n^\alpha(x)$}
{wiki}
For $\alpha>0$, the Gegenbauer polynomial $C_n^\alpha$ is the degree-$n$ polynomial solution of
$$
(1-x^2)y''-(2\alpha+1)xy'+n(n+2\alpha)y=0.
$$
These polynomials are orthogonal on $(-1,1)$ with weight $(1-x^2)^{\alpha-1/2}$.