Relationship between Chebyshev U and hypergeometric 2F1

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

Proof: █