DLMF:7.7.E9 (Q2379)

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DLMF:7.7.E9
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    Statements

    Defining formula
    ∫ 0 x erf ⁡ t ⁢ d t = x ⁢ erf ⁡ x + 1 π ⁢ ( e - x 2 - 1 ) . superscript subscript 0 𝑥 error-function 𝑡 𝑡 𝑥 error-function 𝑥 1 𝜋 superscript 𝑒 superscript 𝑥 2 1 {\displaystyle{\displaystyle\int_{0}^{x}\operatorname{erf}t\mathrm{d}t=x% \operatorname{erf}x+\frac{1}{\sqrt{\pi}}\left(e^{-x^{2}}-1\right).}}
    0 references
    DLMF id
    DLMF:7.7.E9
    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.m2ahdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    error function
    Defining formula
    erf ⁡ z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}
    xml-id
    C7.S2.E1.m2aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
    0 references
    Q11313
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C7.S1.XMD1.m1bdec
    0 references
     
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