DLMF:18.7.E2 (Q5570)

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DLMF:18.7.E2
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    Statements

    Defining formula
    P n ( α , α ) ⁡ ( x ) = ( α + 1 ) n ( 2 ⁢ α + 1 ) n ⁢ C n ( α + 1 2 ) ⁡ ( x ) . Jacobi-polynomial-P 𝛼 𝛼 𝑛 𝑥 Pochhammer 𝛼 1 𝑛 Pochhammer 2 𝛼 1 𝑛 ultraspherical-Gegenbauer-polynomial 𝛼 1 2 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\alpha,\alpha)}_{n}\left(x\right)=\frac{{% \left(\alpha+1\right)_{n}}}{{\left(2\alpha+1\right)_{n}}}C^{(\alpha+\frac{1}{2% })}_{n}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.7.E2
    0 references
    Symbols used
    Q11660
    Defining formula
    P n ( α , β ) ⁡ ( x ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r2.m2aadec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    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.m2aadec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1adec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1adec
    0 references
     
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