DLMF:7.19.E2 (Q2466)

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DLMF:7.19.E2
No description defined

    Statements

    Defining formula
    𝖵 ⁡ ( x , t ) = 1 4 ⁢ π ⁢ t ⁢ ∫ - ∞ ∞ y ⁢ e - ( x - y ) 2 / ( 4 ⁢ t ) 1 + y 2 ⁢ d y . Voigt-V 𝑥 𝑡 1 4 𝜋 𝑡 superscript subscript 𝑦 superscript 𝑒 superscript 𝑥 𝑦 2 4 𝑡 1 superscript 𝑦 2 𝑦 {\displaystyle{\displaystyle\mathsf{V}\left(x,t\right)=\frac{1}{\sqrt{4\pi t}}% \int_{-\infty}^{\infty}\frac{ye^{-(x-y)^{2}/(4t)}}{1+y^{2}}\mathrm{d}y.}}
    0 references
    DLMF id
    DLMF:7.19.E2
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
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    Q11313
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C7.S1.XMD1.m1adec
    0 references
     
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