DLMF:18.7.E15 (Q5583)

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DLMF:18.7.E15
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    C 2 ⁢ n ( λ ) ⁡ ( x ) = ( λ ) n ( 1 2 ) n ⁢ P n ( λ - 1 2 , - 1 2 ) ⁡ ( 2 ⁢ x 2 - 1 ) , ultraspherical-Gegenbauer-polynomial 𝜆 2 𝑛 𝑥 Pochhammer 𝜆 𝑛 Pochhammer 1 2 𝑛 Jacobi-polynomial-P 𝜆 1 2 1 2 𝑛 2 superscript 𝑥 2 1 {\displaystyle{\displaystyle C^{(\lambda)}_{2n}\left(x\right)=\frac{{\left(% \lambda\right)_{n}}}{{\left(\tfrac{1}{2}\right)_{n}}}P^{(\lambda-\frac{1}{2},-% \frac{1}{2})}_{n}\left(2x^{2}-1\right),}}
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    DLMF id
    DLMF:18.7.E15
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