DLMF:1.16.E29 (Q629): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10812 / rank
 
Normal rank
Property / Symbols used: Q10812 / qualifier
 
test:

ℝ {\displaystyle{\displaystyle\mathbb{R}}}

\Reals
Property / Symbols used: Q10812 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r14.m2acdec

Revision as of 15:37, 1 January 2020

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DLMF:1.16.E29
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    Statements

    test
    ℱ ⁢ ( ϕ ) ⁢ ( 𝐱 ) = ℱ ⁢ ϕ ⁢ ( 𝐱 ) = 1 ( 2 ⁢ π ) n / 2 ⁢ ∫ ℝ n ϕ ⁢ ( 𝐭 ) ⁢ e i ⁢ 𝐱 ⋅ 𝐭 ⁢ d 𝐭 , ℱ italic-ϕ 𝐱 ℱ italic-ϕ 𝐱 1 superscript 2 𝜋 𝑛 2 subscript 𝑛 italic-ϕ 𝐭 superscript 𝑒 ⋅ 𝑖 𝐱 𝐭 𝐭 {\displaystyle{\displaystyle\mathscr{F}(\phi)(\mathbf{x})=\mathscr{F}\phi(% \mathbf{x})=\frac{1}{(2\pi)^{n/2}}\int_{{\mathbb{R}^{n}}}\phi(\mathbf{t})e^{i% \mathbf{x}\cdot\mathbf{t}}\mathrm{d}\mathbf{t},}}
    0 references
    DLMF id
    DLMF:1.16.E29
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Q10812
    test
    ℝ {\displaystyle{\displaystyle\mathbb{R}}}
    xml-id
    introduction.Sx4.p2.t1.r14.m2acdec
    0 references
     
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