DLMF:1.16.E32 (Q634)

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DLMF:1.16.E32
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    Statements

    Defining formula
    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}}.}}
    0 references
    DLMF id
    DLMF:1.16.E32
    0 references
    Symbols used
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4aadec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2aadec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1ndec
    0 references
    vector differential operator (locally)
    Defining formula
    𝐃 𝐃 {\displaystyle{\displaystyle\mathbf{D}}}
    xml-id
    C1.S16.XMD16.m1adec
    0 references
     
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