Formula:212

Digital Library of Mathematical Functions ID 1.6.E60

${\displaystyle{\displaystyle\iiint_{V}(f\nabla^{2}g-g\nabla^{2}f)\mathrm{d}V=\iint_{S}\left(f\frac{\partial g}{\partial n}-g\frac{\partial f}{\partial n}\right)\mathrm{d}A,}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$: partial derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\partial\NVar{x}}}$: partial differential of $$x$$
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle S}}$: parameterized surface
• ${\displaystyle{\displaystyle A(S)}}$: area of a parameterized smooth surface $$S$$ (locally)
• ${\displaystyle{\displaystyle V}}$: closed region
 

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