Formula:604

Digital Library of Mathematical Functions ID 1.16.E32

${\displaystyle{\displaystyle P(\mathbf{D})=\sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}\mathbf{D}^{\alpha}=\sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}\left(\frac{1}{\mathrm{i}}\frac{\partial}{\partial x_{1}}\right)^{\alpha_{1}}\dots\left(\frac{1}{\mathrm{i}}\frac{\partial}{\partial x_{n}}\right)^{\alpha_{n}}.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$: partial derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\partial\NVar{x}}}$: partial differential of $$x$$
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle\mathbf{D}}}$: vector differential operator (locally)
• ${\displaystyle{\displaystyle P}}$: polynomial of several variables
• ${\displaystyle{\displaystyle Df}}$:
 

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