DLMF:18.9.E17 (Q5613)

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DLMF:18.9.E17
No description defined

    Statements

    Defining formula
    ( 2 ⁢ n + α + β ) ⁢ ( 1 - x 2 ) ⁢ d d x ⁡ P n ( α , β ) ⁡ ( x ) = n ⁢ ( α - β - ( 2 ⁢ n + α + β ) ⁢ x ) ⁢ P n ( α , β ) ⁡ ( x ) + 2 ⁢ ( n + α ) ⁢ ( n + β ) ⁢ P n - 1 ( α , β ) ⁡ ( x ) , 2 𝑛 𝛼 𝛽 1 superscript 𝑥 2 derivative 𝑥 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 𝑛 𝛼 𝛽 2 𝑛 𝛼 𝛽 𝑥 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 2 𝑛 𝛼 𝑛 𝛽 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 𝑥 {\displaystyle{\displaystyle(2n+\alpha+\beta)(1-x^{2})\frac{\mathrm{d}}{% \mathrm{d}x}P^{(\alpha,\beta)}_{n}\left(x\right)=n\left(\alpha-\beta-(2n+% \alpha+\beta)x\right)P^{(\alpha,\beta)}_{n}\left(x\right)+2(n+\alpha)(n+\beta)% P^{(\alpha,\beta)}_{n-1}\left(x\right),}}
    0 references
    DLMF id
    DLMF:18.9.E17
    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
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    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2abdec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1qdec
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    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1pdec
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