# Gegenbauer C

The Gegenbauer polynomial $C_n^{\lambda}$ of degree $n \in \{0,1,2,\ldots\}$ and order $\lambda$ defined by $$C_n^{\lambda}(x)=\displaystyle\sum_{k=0}^{\left\lfloor \frac{n}{2} \right\rfloor} \dfrac{(-1)^k\Gamma(n-k+\lambda)}{\Gamma(\lambda)k!(n-2k)!} (2x)^{n-2k},$$ where $\left\lfloor \frac{n}{2} \right\rfloor$ denotes the floor function, $\Gamma$ denotes gamma, and $k!$ denotes the factorial.