1.15.E36 (Q548)

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1.15.E36
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    Statements

    DLMF defining formula
    h ⁢ ( x , y ) = 1 2 ⁢ π ⁢ ∫ - ∞ ∞ e - y ⁢ | t | ⁢ e - i ⁢ x ⁢ t ⁢ F ⁢ ( t ) ⁢ d t , ℎ 𝑥 𝑦 1 2 𝜋 subscript superscript superscript 𝑒 𝑦 𝑡 superscript 𝑒 𝑖 𝑥 𝑡 𝐹 𝑡 𝑡 {\displaystyle{\displaystyle h(x,y)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-% \infty}e^{-y|t|}e^{-ixt}F(t)\mathrm{d}t,}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
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    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
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    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
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    Fourier transform of f ( t )
    DLMF defining formula
    F ⁢ ( x ) 𝐹 𝑥 {\displaystyle{\displaystyle F(x)}}
    xml-id
    C1.S14.XMD1.m1dec
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    function
    DLMF defining formula
    h ⁢ ( x , y ) ℎ 𝑥 𝑦 {\displaystyle{\displaystyle h(x,y)}}
    xml-id
    C1.S15.XMD8.m1dec
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    Identifiers

     
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