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DLMF:1.14.E8 - MaRDI portal

DLMF:1.14.E8 (Q469)

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DLMF:1.14.E8
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    Statements

    DLMF defining formula
    ∫ - ∞ ∞ | F ⁢ ( x ) | 2 ⁢ d x = ∫ - ∞ ∞ | f ⁢ ( t ) | 2 ⁢ d t . subscript superscript superscript 𝐹 𝑥 2 𝑥 subscript superscript superscript 𝑓 𝑡 2 𝑡 {\displaystyle{\displaystyle\int^{\infty}_{-\infty}|F(x)|^{2}\mathrm{d}x=\int^% {\infty}_{-\infty}|f(t)|^{2}\mathrm{d}t.}}
    0 references
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
    0 references
    Fourier transform of f ( t )
    DLMF defining formula
    F ⁢ ( x ) 𝐹 𝑥 {\displaystyle{\displaystyle F(x)}}
    xml-id
    C1.S14.XMD1.m1edec
    0 references

    Identifiers

     
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