DLMF:18.7.E9 (Q5577)

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DLMF:18.7.E9
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    Statements

    Defining formula
    P n ⁡ ( x ) = C n ( 1 2 ) ⁡ ( x ) = P n ( 0 , 0 ) ⁡ ( x ) . Legendre-spherical-polynomial 𝑛 𝑥 ultraspherical-Gegenbauer-polynomial 1 2 𝑛 𝑥 Jacobi-polynomial-P 0 0 𝑛 𝑥 {\displaystyle{\displaystyle P_{n}\left(x\right)=C^{(\frac{1}{2})}_{n}\left(x% \right)=P^{(0,0)}_{n}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.7.E9
    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.m2afdec
    0 references
    Q10920
    Defining formula
    P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r10.m2adec
    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.m2acdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1hdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1hdec
    0 references
     
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