DLMF:18.14.E7 (Q5670)

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DLMF:18.14.E7
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    Statements

    test
    ( n + λ ) 1 - λ ⁢ ( 1 - x 2 ) 1 2 ⁢ λ ⁢ | C n ( λ ) ⁡ ( x ) | < 2 1 - λ Γ ⁡ ( λ ) , superscript 𝑛 𝜆 1 𝜆 superscript 1 superscript 𝑥 2 1 2 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 superscript 2 1 𝜆 Euler-Gamma 𝜆 {\displaystyle{\displaystyle{(n+\lambda)^{1-\lambda}(1-x^{2})^{\frac{1}{2}% \lambda}|C^{(\lambda)}_{n}\left(x\right)|<\frac{2^{1-\lambda}}{\Gamma\left(% \lambda\right)}},}}
    0 references
    DLMF id
    DLMF:18.14.E7
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    constraint
    0 < λ < 1 0 𝜆 1 {\displaystyle{\displaystyle 0<\lambda<1}}
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
     
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