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1.16.E32 - MaRDI portal
Statements
P
(
𝐃
)
=
∑
𝜶
c
𝜶
𝐃
α
=
∑
𝜶
c
𝜶
(
1
i
∂
∂
x
1
)
α
1
…
(
1
i
∂
∂
x
n
)
α
n
.
𝑃
𝐃
subscript
𝜶
subscript
𝑐
𝜶
superscript
𝐃
𝛼
subscript
𝜶
subscript
𝑐
𝜶
superscript
1
imaginary-unit
partial-derivative
subscript
𝑥
1
subscript
𝛼
1
…
superscript
1
imaginary-unit
partial-derivative
subscript
𝑥
𝑛
subscript
𝛼
𝑛
{\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}}.}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∂
f
∂
x
partial-derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
∂
x
𝑥
{\displaystyle{\displaystyle\partial\NVar{x}}}
n
𝑛
{\displaystyle{\displaystyle n}}
𝐃
𝐃
{\displaystyle{\displaystyle\mathbf{D}}}
P
𝑃
{\displaystyle{\displaystyle P}}
D
f
𝐷
𝑓
{\displaystyle{\displaystyle Df}}