DLMF:14.7.E9 (Q4761)

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DLMF:14.7.E9
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    Statements

    Defining formula
    𝖰 n m ⁡ ( x ) = ( - 1 ) m ⁢ ( 1 - x 2 ) m / 2 ⁢ d m d x m ⁡ 𝖰 n ⁡ ( x ) , Ferrers-Legendre-Q-first-kind 𝑚 𝑛 𝑥 superscript 1 𝑚 superscript 1 superscript 𝑥 2 𝑚 2 derivative 𝑥 𝑚 shorthand-Ferrers-Legendre-Q-first-kind 𝑛 𝑥 {\displaystyle{\displaystyle\mathsf{Q}^{m}_{n}\left(x\right)=(-1)^{m}\left(1-x% ^{2}\right)^{m/2}\frac{{\mathrm{d}}^{m}}{{\mathrm{d}x}^{m}}\mathsf{Q}_{n}\left% (x\right),}}
    0 references
    DLMF id
    DLMF:14.7.E9
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    Symbols used
    Ferrers function of the second kind
    Defining formula
    𝖰 ν μ ⁡ ( x ) Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E2.m2aadec
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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.m2aadec
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    Q11596
    Defining formula
    𝖰 ν ⁡ ( x ) = 𝖰 ν 0 ⁡ ( x ) shorthand-Ferrers-Legendre-Q-first-kind 𝜈 𝑥 Ferrers-Legendre-Q-first-kind 0 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{Q}^{0}_{\nu}\left(x\right)}}
    xml-id
    C14.S2.SS2.p2.m4aadec
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    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1hdec
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    Q11593
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1adec
    0 references
    Q11602
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1gdec
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