# Relationship between Chebyshev T and hypergeometric 2F1

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

Proof: