DLMF:1.16.E34 (Q638)

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DLMF:1.16.E34
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    Statements

    Defining formula
    ℱ ⁢ ( P ⁢ ϕ ) ⁢ ( 𝐱 ) = P ⁢ ( 𝐃 ) ⁢ ℱ ⁢ ϕ ⁢ ( 𝐱 ) . ℱ 𝑃 italic-ϕ 𝐱 𝑃 𝐃 ℱ italic-ϕ 𝐱 {\displaystyle{\displaystyle\mathscr{F}(P\phi)(\mathbf{x})=P(\mathbf{D})% \mathscr{F}\phi(\mathbf{x}).}}
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    DLMF id
    DLMF:1.16.E34
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
    0 references
    Q10812
    Defining formula
    ℝ {\displaystyle{\displaystyle\mathbb{R}}}
    xml-id
    introduction.Sx4.p2.t1.r14.m2aedec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1pdec
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    Q10912
    Defining formula
    ϕ ⁢ ( x 1 , x 2 , … , x n ) italic-ϕ subscript 𝑥 1 subscript 𝑥 2 … subscript 𝑥 𝑛 {\displaystyle{\displaystyle\phi(x_{1},x_{2},\dots,x_{n})}}
    xml-id
    C1.S16.XMD13.m1edec
    0 references
    Fourier transform of a test function (locally)
    Defining formula
    ℱ ⁢ ( ϕ ) ℱ italic-ϕ {\displaystyle{\displaystyle\mathscr{F}(\phi)}}
    xml-id
    C1.S16.XMD15.m1bdec
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    vector differential operator (locally)
    Defining formula
    𝐃 𝐃 {\displaystyle{\displaystyle\mathbf{D}}}
    xml-id
    C1.S16.XMD16.m1cdec
    0 references
    Q10913
    Defining formula
    P 𝑃 {\displaystyle{\displaystyle P}}
    xml-id
    C1.S16.XMD17.m1cdec
    0 references
    Q10909
    Defining formula
    D ⁢ f 𝐷 𝑓 {\displaystyle{\displaystyle Df}}
    xml-id
    C1.S16.XMD6.m1jdec
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