DLMF:1.6.E60 (Q241): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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
 
Defining formula:

∂ ⁡ 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.m4ajdec

Revision as of 16:01, 1 January 2020

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DLMF:1.6.E60
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    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
     
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