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DLMF:7.5.E13 - MaRDI portal

DLMF:7.5.E13 (Q3057)

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DLMF:7.5.E13
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    Statements

    DLMF defining formula
    G ⁡ ( x ) = π ⁢ F ⁡ ( x ) - 1 2 ⁢ e - x 2 ⁢ Ei ⁡ ( x 2 ) , Goodwin-Staton-integral 𝑥 𝜋 Dawsons-integral 𝑥 1 2 superscript 𝑒 superscript 𝑥 2 exponential-integral-Ei superscript 𝑥 2 {\displaystyle{\displaystyle G\left(x\right)=\sqrt{\pi}F\left(x\right)-\tfrac{% 1}{2}e^{-x^{2}}\mathrm{Ei}\left(x^{2}\right),}}
    0 references
    constraint
    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
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    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.m2aadec
    0 references
    Goodwin–Staton integral
    DLMF defining formula
    G ⁡ ( z ) Goodwin-Staton-integral 𝑧 {\displaystyle{\displaystyle G\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E12.m2adec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    Q11277
    DLMF defining formula
    Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.SS1.p3.m2adec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C7.S1.XMD1.m1bdec
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    Identifiers

     
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