DLMF:18.7.E16 (Q5584)

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DLMF:18.7.E16
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    C 2 ⁢ n + 1 ( λ ) ⁡ ( x ) = ( λ ) n + 1 ( 1 2 ) n + 1 ⁢ x ⁢ P n ( λ - 1 2 , 1 2 ) ⁡ ( 2 ⁢ x 2 - 1 ) . ultraspherical-Gegenbauer-polynomial 𝜆 2 𝑛 1 𝑥 Pochhammer 𝜆 𝑛 1 Pochhammer 1 2 𝑛 1 𝑥 Jacobi-polynomial-P 𝜆 1 2 1 2 𝑛 2 superscript 𝑥 2 1 {\displaystyle{\displaystyle C^{(\lambda)}_{2n+1}\left(x\right)=\frac{{\left(% \lambda\right)_{n+1}}}{{\left(\frac{1}{2}\right)_{n+1}}}xP^{(\lambda-\frac{1}{% 2},\frac{1}{2})}_{n}\left(2x^{2}-1\right).}}
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    DLMF:18.7.E16
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