DLMF:1.5.E17 (Q140)

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DLMF:1.5.E17
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${\displaystyle{\displaystyle\nabla^{2}f=\frac{{\partial}^{2}f}{{\partial x}^{2% }}+\frac{{\partial}^{2}f}{{\partial y}^{2}}+\frac{{\partial}^{2}f}{{\partial z% }^{2}}={\frac{1}{\rho^{2}}\frac{\partial}{\partial\rho}\left(\rho^{2}\frac{% \partial f}{\partial\rho}\right)+\frac{1}{\rho^{2}{\sin^{2}}\theta}\frac{{% \partial}^{2}f}{{\partial\phi}^{2}}}+\frac{1}{\rho^{2}\sin\theta}\frac{% \partial}{\partial\theta}\left(\sin\theta\frac{\partial f}{\partial\theta}% \right).}}$
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DLMF:1.5.E17
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${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$
C1.S5.E3.m4ajdec
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${\displaystyle{\displaystyle\partial\NVar{x}}}$
C1.S5.E3.m2akdec
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${\displaystyle{\displaystyle\sin\NVar{z}}}$
C4.S14.E1.m2aedec
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${\displaystyle{\displaystyle z}}$
C1.S1.XMD1.m1cdec
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${\displaystyle{\displaystyle\phi}}$
C1.S5.XMD10.m1gdec
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${\displaystyle{\displaystyle\rho}}$
${\displaystyle{\displaystyle\theta}}$