DLMF:1.6.E59 (Q240)

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DLMF:1.6.E59
No description defined

    Statements

    Defining formula
    ∭ V ( f ⁢ ∇ 2 ⁡ g + ∇ ⁡ f ⋅ ∇ ⁡ g ) ⁢ d V = ∬ S f ⁢ ∂ ⁡ g ∂ ⁡ n ⁢ d A , subscript triple-integral 𝑉 𝑓 superscript ∇ 2 𝑔 ⋅ ∇ 𝑓 ∇ 𝑔 𝑉 subscript double-integral 𝑆 𝑓 partial-derivative 𝑔 𝑛 𝐴 {\displaystyle{\displaystyle\iiint_{V}(f\nabla^{2}g+\nabla f\cdot\nabla g)% \mathrm{d}V=\iint_{S}f\frac{\partial g}{\partial n}\mathrm{d}A,}}
    0 references
    DLMF id
    DLMF:1.6.E59
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aqdec
    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.m4aidec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2ajdec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1adec
    0 references
    Q10799
    Defining formula
    S 𝑆 {\displaystyle{\displaystyle S}}
    xml-id
    C1.S6.XMD12.m1hdec
    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.m1ddec
    0 references
    Q10804
    Defining formula
    V 𝑉 {\displaystyle{\displaystyle V}}
    xml-id
    C1.S6.XMD19.m1adec
    0 references
     
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