DLMF:18.9.E16 (Q5612)

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DLMF:18.9.E16
No description defined

    Statements

    Defining formula
    d d x ⁡ ( ( 1 - x ) α ⁢ ( 1 + x ) β ⁢ P n ( α , β ) ⁡ ( x ) ) = - 2 ⁢ ( n + 1 ) ⁢ ( 1 - x ) α - 1 ⁢ ( 1 + x ) β - 1 ⁢ P n + 1 ( α - 1 , β - 1 ) ⁡ ( x ) . derivative 𝑥 superscript 1 𝑥 𝛼 superscript 1 𝑥 𝛽 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 2 𝑛 1 superscript 1 𝑥 𝛼 1 superscript 1 𝑥 𝛽 1 Jacobi-polynomial-P 𝛼 1 𝛽 1 𝑛 1 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}\left((1-x)^{\alpha}% (1+x)^{\beta}P^{(\alpha,\beta)}_{n}\left(x\right)\right)=-2(n+1)(1-x)^{\alpha-% 1}(1+x)^{\beta-1}P^{(\alpha-1,\beta-1)}_{n+1}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.9.E16
    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.m2aedec
    0 references
    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.m2aadec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1pdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1odec
    0 references
     
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