DLMF:1.13.E20 (Q486): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10760 / rank
 
Normal rank
Property / Symbols used: Q10760 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q10760 / qualifier
 
xml-id: C1.S1.XMD1.m1qdec
Property / Symbols used
 
Property / Symbols used: Q10880 / rank
 
Normal rank
Property / Symbols used: Q10880 / qualifier
 
Defining formula:

ζ ⁢ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}

\zeta(z)
Property / Symbols used: Q10880 / qualifier
 
xml-id: C1.S13.XMD26.m1bdec

Latest revision as of 16:20, 1 January 2020

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DLMF:1.13.E20
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    Statements

    Defining formula
    { z , ζ } = - 2 ⁢ z ˙ 1 / 2 ⁢ d 2 d ζ 2 ⁡ ( z ˙ - 1 / 2 ) = z ˙˙˙ z ˙ - 3 2 ⁢ ( z ¨ z ˙ ) 2 . Schwarzian 𝑧 𝜁 2 superscript ˙ 𝑧 1 2 derivative 𝜁 2 superscript ˙ 𝑧 1 2 ˙˙˙ 𝑧 ˙ 𝑧 3 2 superscript ¨ 𝑧 ˙ 𝑧 2 {\displaystyle{\displaystyle\left\{z,\zeta\right\}=-2\dot{z}^{\ifrac{1}{2}}% \frac{{\mathrm{d}}^{2}}{{\mathrm{d}\zeta}^{2}}(\dot{z}^{-\ifrac{1}{2}})=\frac{% \dddot{z}}{\dot{z}}-\frac{3}{2}\left(\frac{\ddot{z}}{\dot{z}}\right)^{2}.}}
    0 references
    DLMF id
    DLMF:1.13.E20
    0 references
    Symbols used
    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.m2agdec
    0 references
    Q10760
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1qdec
    0 references
    Q10880
    Defining formula
    ζ ⁢ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}
    xml-id
    C1.S13.XMD26.m1bdec
    0 references
     
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