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DLMF:8.4.E3 - MaRDI portal

DLMF:8.4.E3 (Q3195)

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DLMF:8.4.E3
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    Statements

    DLMF defining formula
    γ * ⁡ ( 1 2 , - z 2 ) = 2 ⁢ e z 2 z ⁢ π ⁢ F ⁡ ( z ) . incomplete-gamma-star 1 2 superscript 𝑧 2 2 superscript 𝑒 superscript 𝑧 2 𝑧 𝜋 Dawsons-integral 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\tfrac{1}{2},-z^{2}\right)=\frac{2% e^{z^{2}}}{z\sqrt{\pi}}F\left(z\right).}}
    0 references
    Symbols used
    Dawson’s integral
    DLMF defining formula
    F ⁡ ( z ) Dawsons-integral 𝑧 {\displaystyle{\displaystyle F\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E5.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    incomplete gamma function
    DLMF defining formula
    γ * ⁡ ( a , z ) incomplete-gamma-star 𝑎 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E6.m2aadec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1adec
    0 references

    Identifiers

     
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