DLMF:18.5.E9 (Q5517)

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DLMF:18.5.E9
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    Statements

    test
    C n ( λ ) ⁡ ( x ) = ( 2 ⁢ λ ) n n ! ⁢ F 1 2 ⁡ ( - n , n + 2 ⁢ λ λ + 1 2 ; 1 - x 2 ) , ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 Pochhammer 2 𝜆 𝑛 𝑛 Gauss-hypergeometric-F-as-2F1 𝑛 𝑛 2 𝜆 𝜆 1 2 1 𝑥 2 {\displaystyle{\displaystyle C^{(\lambda)}_{n}\left(x\right)=\frac{{\left(2% \lambda\right)_{n}}}{n!}{{}_{2}F_{1}}\left({-n,n+2\lambda\atop\lambda+\tfrac{1% }{2}};\frac{1-x}{2}\right),}}
    0 references
    DLMF id
    DLMF:18.5.E9
    0 references
    Symbols used
    Q11581
    test
    F 1 2 ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}
    xml-id
    C16.S2.m5abdec
    0 references
     
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