DLMF:21.9.E4 (Q6920): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
 
test:

∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}

\pderiv{\NVar{f}}{\NVar{x}}
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S5.E3.m4adec
Property / Symbols used
 
Property / Symbols used: partial differential of $$x$$ / rank
 
Normal rank
Property / Symbols used: partial differential of $$x$$ / qualifier
 
test:

∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}

\pdiff{\NVar{x}}
Property / Symbols used: partial differential of $$x$$ / qualifier
 
xml-id: C1.S5.E3.m2adec
Property / Symbols used
 
Property / Symbols used: Q11960 / rank
 
Normal rank
Property / Symbols used: Q11960 / qualifier
 
test:

𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}

\boldsymbol{{\Omega}}
Property / Symbols used: Q11960 / qualifier
 
xml-id: C21.S1.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q11982 / rank
 
Normal rank
Property / Symbols used: Q11982 / qualifier
 
test:

u ⁢ ( x , y , t ) 𝑢 𝑥 𝑦 𝑡 {\displaystyle{\displaystyle u(x,y,t)}}

u(x,y,t)
Property / Symbols used: Q11982 / qualifier
 
xml-id: C21.S9.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11983 / rank
 
Normal rank
Property / Symbols used: Q11983 / qualifier
 
test:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q11983 / qualifier
 
xml-id: C21.S9.XMD2.m1dec

Latest revision as of 13:54, 2 January 2020

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DLMF:21.9.E4
No description defined

    Statements

    test
    u ⁢ ( x , y , t ) = c + 2 ⁢ ∂ 2 ∂ ⁡ x 2 ⁡ ln ⁡ ( θ ⁡ ( 𝐤 ⁢ x + 𝐥 ⁢ y + 𝝎 ⁢ t + ϕ | 𝛀 ) ) , 𝑢 𝑥 𝑦 𝑡 𝑐 2 partial-derivative 𝑥 2 Riemann-theta 𝐤 𝑥 𝐥 𝑦 𝝎 𝑡 bold-italic-ϕ 𝛀 {\displaystyle{\displaystyle u(x,y,t)=c+2\frac{{\partial}^{2}}{{\partial x}^{2% }}\ln\left(\theta\left(\mathbf{k}x+\mathbf{l}y+\boldsymbol{{\omega}}t+% \boldsymbol{{\phi}}\middle|\boldsymbol{{\Omega}}\right)\right),}}
    0 references
    DLMF id
    DLMF:21.9.E4
    0 references
    Symbols used
    Riemann theta function
    test
    θ ⁡ ( 𝐳 | 𝛀 ) Riemann-theta 𝐳 𝛀 {\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{% \boldsymbol{{\Omega}}}\right)}}
    xml-id
    C21.S2.E1.m2adec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    partial derivative of $$f$$ with respect to $$x$$
    test
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4adec
    0 references
    partial differential of $$x$$
    test
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2adec
    0 references
    Q11960
    test
    𝛀 𝛀 {\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}
    xml-id
    C21.S1.XMD3.m1dec
    0 references
    Q11982
    test
    u ⁢ ( x , y , t ) 𝑢 𝑥 𝑦 𝑡 {\displaystyle{\displaystyle u(x,y,t)}}
    xml-id
    C21.S9.XMD1.m1cdec
    0 references
    Q11983
    test
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C21.S9.XMD2.m1dec
    0 references
     
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