DLMF:36.4.E4 (Q9876): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12742 / rank
 
Normal rank
Property / Symbols used: Q12742 / qualifier
 
Defining formula:

t 𝑡 {\displaystyle{\displaystyle t}}

t
Property / Symbols used: Q12742 / qualifier
 
xml-id: C36.S1.XMD5.m1cdec

Revision as of 15:08, 2 January 2020

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DLMF:36.4.E4
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    Statements

    Defining formula
    ∂ 2 ∂ ⁡ s 2 ⁡ Φ ( U ) ⁡ ( s , t ; 𝐱 ) ⁢ ∂ 2 ∂ ⁡ t 2 ⁡ Φ ( U ) ⁡ ( s , t ; 𝐱 ) - ( ∂ 2 ⁡ ∂ ⁡ s ⁢ ∂ ⁡ t ⁢ Φ ( U ) ⁡ ( s , t ; 𝐱 ) ) 2 = 0 . partial-derivative 𝑠 2 umbilic-catastrophe 𝑠 𝑡 𝐱 partial-derivative 𝑡 2 umbilic-catastrophe 𝑠 𝑡 𝐱 superscript 2 𝑠 𝑡 umbilic-catastrophe 𝑠 𝑡 𝐱 2 0 {\displaystyle{\displaystyle\frac{{\partial}^{2}}{{\partial s}^{2}}\Phi^{(% \mathrm{U})}\left(s,t;\mathbf{x}\right)\frac{{\partial}^{2}}{{\partial t}^{2}}% \Phi^{(\mathrm{U})}\left(s,t;\mathbf{x}\right)-\left(\frac{{\partial}^{2}}{% \partial s\partial t}\Phi^{(\mathrm{U})}\left(s,t;\mathbf{x}\right)\right)^{2}% =0.}}
    0 references
    DLMF id
    DLMF:36.4.E4
    0 references
    Symbols used
    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4acdec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2acdec
    0 references
    Q12749
    Defining formula
    Φ ( U ) ⁡ ( s , t ; 𝐱 ) umbilic-catastrophe 𝑠 𝑡 𝐱 {\displaystyle{\displaystyle\Phi^{(\mathrm{U})}\left(\NVar{s},\NVar{t};\NVar{% \mathbf{x}}\right)}}
    xml-id
    C36.S2.Px2.m2aadec
    0 references
    Q12742
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C36.S1.XMD5.m1cdec
    0 references
     
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