DLMF:14.6.E4 (Q4746)

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DLMF:14.6.E4
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    Statements

    test
    Q ν m ⁡ ( x ) = ( x 2 - 1 ) m / 2 ⁢ d m Q ν ⁡ ( x ) d x m , Legendre-Q-second-kind 𝑚 𝜈 𝑥 superscript superscript 𝑥 2 1 𝑚 2 derivative shorthand-Legendre-Q-second-kind 𝜈 𝑥 𝑥 𝑚 {\displaystyle{\displaystyle Q^{m}_{\nu}\left(x\right)=\left(x^{2}-1\right)^{m% /2}\frac{{\mathrm{d}}^{m}Q_{\nu}\left(x\right)}{{\mathrm{d}x}^{m}},}}
    0 references
    DLMF id
    DLMF:14.6.E4
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    Symbols used
    Q11470
    test
    Q ν μ ⁡ ( z ) Legendre-Q-second-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle Q^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m2adec
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    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2acdec
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    Q11448
    test
    Q ν ⁡ ( z ) = Q ν 0 ⁡ ( z ) shorthand-Legendre-Q-second-kind 𝜈 𝑧 Legendre-Q-second-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}% \left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m5adec
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    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1cdec
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    Q11593
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1cdec
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