# Relationship between Legendre polynomial and hypergeometric 2F1

Theorem: The following formula holds: $$P_n(x) = {}_2F_1 \left( -n, n+2; \dfrac{3}{2}; \dfrac{1-x}{2} \right),$$ where $P_n$ denotes a Legendre polynomial and ${}_2F_1$ denotes the hypergeometric pFq.