Formula:103

Digital Library of Mathematical Functions ID 1.5.E13

${\displaystyle{\displaystyle\nabla^{2}f=\frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{\partial}^{2}f}{{\partial y}^{2}}=\frac{{\partial}^{2}f}{{\partial r}^{2}}+\frac{1}{r}\frac{\partial f}{\partial r}+\frac{1}{r^{2}}\frac{{\partial}^{2}f}{{\partial\phi}^{2}}.}}$

Symbols List

• ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$: partial derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\partial\NVar{x}}}$: partial differential of $$x$$
• ${\displaystyle{\displaystyle\phi}}$: longitude
• ${\displaystyle{\displaystyle r}}$: radius
 

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