DLMF:1.13.E19 (Q485)

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DLMF:1.13.E19
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    Statements

    test
    d 2 U d ζ 2 = ( z ˙ 2 ⁢ H ⁢ ( z ) - 1 2 ⁢ { z , ζ } ) ⁢ U . derivative 𝑈 𝜁 2 superscript ˙ 𝑧 2 𝐻 𝑧 1 2 Schwarzian 𝑧 𝜁 𝑈 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}U}{{\mathrm{d}\zeta}^{2}}=% \left(\dot{z}^{2}H(z)-\tfrac{1}{2}\left\{z,\zeta\right\}\right)U.}}
    0 references
    DLMF id
    DLMF:1.13.E19
    0 references
    Symbols used
    Schwarzian derivative
    test
    { z , ζ } Schwarzian 𝑧 𝜁 {\displaystyle{\displaystyle\left\{\NVar{z},\NVar{\zeta}\right\}}}
    xml-id
    C1.S13.E20.m2adec
    0 references
    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.m2afdec
    0 references
    Q10760
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1pdec
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    DLMF:1.13.E15
    test
    H ⁢ ( z ) 𝐻 𝑧 {\displaystyle{\displaystyle H(z)}}
    xml-id
    C1.S13.XMD24.m1bdec
    0 references
     
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