DLMF:1.6.E60 (Q241)

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DLMF:1.6.E60
No description defined

    Statements

    Defining formula
    ∭ V ( f ⁢ ∇ 2 ⁡ g - g ⁢ ∇ 2 ⁡ f ) ⁢ d V = ∬ S ( f ⁢ ∂ ⁡ g ∂ ⁡ n - g ⁢ ∂ ⁡ f ∂ ⁡ n ) ⁢ d A , subscript triple-integral 𝑉 𝑓 superscript ∇ 2 𝑔 𝑔 superscript ∇ 2 𝑓 𝑉 subscript double-integral 𝑆 𝑓 partial-derivative 𝑔 𝑛 𝑔 partial-derivative 𝑓 𝑛 𝐴 {\displaystyle{\displaystyle\iiint_{V}(f\nabla^{2}g-g\nabla^{2}f)\mathrm{d}V=% \iint_{S}\left(f\frac{\partial g}{\partial n}-g\frac{\partial f}{\partial n}% \right)\mathrm{d}A,}}
    0 references
    DLMF id
    DLMF:1.6.E60
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ardec
    0 references
    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.m4ajdec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2akdec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1bdec
    0 references
    Q10799
    Defining formula
    S 𝑆 {\displaystyle{\displaystyle S}}
    xml-id
    C1.S6.XMD12.m1idec
    0 references
    area of a parameterized smooth surface $$S$$ (locally)
    Defining formula
    A ⁢ ( S ) 𝐴 𝑆 {\displaystyle{\displaystyle A(S)}}
    xml-id
    C1.S6.XMD15.m1edec
    0 references
    Q10804
    Defining formula
    V 𝑉 {\displaystyle{\displaystyle V}}
    xml-id
    C1.S6.XMD19.m1bdec
    0 references
     
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