DLMF:1.5.E13 (Q132)

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DLMF:1.5.E13
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    2 f = 2 f x 2 + 2 f y 2 = 2 f r 2 + 1 r f r + 1 r 2 2 f ϕ 2 . superscript 2 𝑓 partial-derivative 𝑓 𝑥 2 partial-derivative 𝑓 𝑦 2 partial-derivative 𝑓 𝑟 2 1 𝑟 partial-derivative 𝑓 𝑟 1 superscript 𝑟 2 partial-derivative 𝑓 italic-ϕ 2 {\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}}.}}
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    DLMF:1.5.E13
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