DLMF:18.1.E1 (Q5486)

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DLMF:18.1.E1
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    C n ( 0 ) ⁡ ( x ) = 2 n ⁢ T n ⁡ ( x ) = 2 ⁢ ( n - 1 ) ! ( 1 2 ) n ⁢ P n ( - 1 2 , - 1 2 ) ⁡ ( x ) , ultraspherical-Gegenbauer-polynomial 0 𝑛 𝑥 2 𝑛 Chebyshev-polynomial-first-kind-T 𝑛 𝑥 2 𝑛 1 Pochhammer 1 2 𝑛 Jacobi-polynomial-P 1 2 1 2 𝑛 𝑥 {\displaystyle{\displaystyle C^{(0)}_{n}\left(x\right)=\frac{2}{n}T_{n}\left(x% \right)=\frac{2(n-1)!}{{\left(\tfrac{1}{2}\right)_{n}}}P^{(-\frac{1}{2},-\frac% {1}{2})}_{n}\left(x\right),}}
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    DLMF:18.1.E1
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