DLMF:7.6.E2 (Q2361)

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DLMF:7.6.E2
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    Statements

    Defining formula
    erf ⁡ z = 2 π ⁢ e - z 2 ⁢ ∑ n = 0 ∞ 2 n ⁢ z 2 ⁢ n + 1 1 ⋅ 3 ⁢ ⋯ ⁢ ( 2 ⁢ n + 1 ) , error-function 𝑧 2 𝜋 superscript 𝑒 superscript 𝑧 2 superscript subscript 𝑛 0 superscript 2 𝑛 superscript 𝑧 2 𝑛 1 ⋅ 1 3 ⋯ 2 𝑛 1 {\displaystyle{\displaystyle\operatorname{erf}z=\frac{2}{\sqrt{\pi}}e^{-z^{2}}% \sum_{n=0}^{\infty}\frac{2^{n}z^{2n+1}}{1\cdot 3\cdots(2n+1)},}}
    0 references
    DLMF id
    DLMF:7.6.E2
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    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
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    error function
    Defining formula
    erf ⁡ z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}
    xml-id
    C7.S2.E1.m2aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    Q11312
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1adec
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    Q11314
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C7.S1.XMD3.m1adec
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