DLMF:1.6.E54 (Q235): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aldec
Property / Symbols used
 
Property / Symbols used: Q10799 / rank
 
Normal rank
Property / Symbols used: Q10799 / qualifier
 
test:

S 𝑆 {\displaystyle{\displaystyle S}}

S
Property / Symbols used: Q10799 / qualifier
 
xml-id: C1.S6.XMD12.m1ddec
Property / Symbols used
 
Property / Symbols used: parameterization (locally) / rank
 
Normal rank
Property / Symbols used: parameterization (locally) / qualifier
 
test:

𝚽 ⁢ ( x , y , z ) 𝚽 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle\boldsymbol{{\Phi}}(x,y,z)}}

\boldsymbol{{\Phi}}(x,y,z)
Property / Symbols used: parameterization (locally) / qualifier
 
xml-id: C1.S6.XMD13.m1adec

Latest revision as of 15:01, 1 January 2020

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DLMF:1.6.E54
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    Statements

    test
    ∬ S f ⁢ ( x , y , z ) ⁢ d S = ∬ D f ⁢ ( 𝚽 ⁢ ( u , v ) ) ⁢ ∥ 𝐓 u × 𝐓 v ∥ ⁢ d u ⁢ d v . subscript double-integral 𝑆 𝑓 𝑥 𝑦 𝑧 𝑆 subscript double-integral 𝐷 𝑓 𝚽 𝑢 𝑣 norm subscript 𝐓 𝑢 subscript 𝐓 𝑣 𝑢 𝑣 {\displaystyle{\displaystyle\iint_{S}f(x,y,z)\mathrm{d}S=\iint_{D}f(% \boldsymbol{{\Phi}}(u,v))\|\mathbf{T}_{u}\times\mathbf{T}_{v}\|\mathrm{d}u% \mathrm{d}v.}}
    0 references
    DLMF id
    DLMF:1.6.E54
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
    0 references
    Q10799
    test
    S 𝑆 {\displaystyle{\displaystyle S}}
    xml-id
    C1.S6.XMD12.m1ddec
    0 references
    parameterization (locally)
    test
    𝚽 ⁢ ( x , y , z ) 𝚽 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle\boldsymbol{{\Phi}}(x,y,z)}}
    xml-id
    C1.S6.XMD13.m1adec
    0 references
     
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