DLMF:18.14.E4 (Q5667)

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DLMF:18.14.E4
No description defined

    Statements

    Defining formula
    | C n ( λ ) ⁡ ( x ) | ≤ C n ( λ ) ⁡ ( 1 ) = ( 2 ⁢ λ ) n n ! , ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 1 Pochhammer 2 𝜆 𝑛 𝑛 {\displaystyle{\displaystyle|C^{(\lambda)}_{n}\left(x\right)|\leq C^{(\lambda)% }_{n}\left(1\right)=\frac{{\left(2\lambda\right)_{n}}}{n!},}}
    0 references
    DLMF id
    DLMF:18.14.E4
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    constraint
    λ > 0 𝜆 0 {\displaystyle{\displaystyle\lambda>0}}
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    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1abdec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
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    Q11475
    Defining formula
    C n ( λ ) ⁡ ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r3.m2adec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1cdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1cdec
    0 references
     
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