DLMF:8.4.E1 (Q2495)

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DLMF:8.4.E1
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    Statements

    test
    γ ⁡ ( 1 2 , z 2 ) = 2 ⁢ ∫ 0 z e - t 2 ⁢ d t = π ⁢ erf ⁡ ( z ) , incomplete-gamma 1 2 superscript 𝑧 2 2 superscript subscript 0 𝑧 superscript 𝑒 superscript 𝑡 2 𝑡 𝜋 error-function 𝑧 {\displaystyle{\displaystyle\gamma\left(\tfrac{1}{2},z^{2}\right)=2\int_{0}^{z% }e^{-t^{2}}\mathrm{d}t=\sqrt{\pi}\operatorname{erf}\left(z\right),}}
    0 references
    DLMF id
    DLMF:8.4.E1
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    error function
    test
    erf ⁡ z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}
    xml-id
    C7.S2.E1.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    incomplete gamma function
    test
    γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E1.m2adec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
     
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