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DLMF:7.2.E2 - MaRDI portal

DLMF:7.2.E2 (Q3020)

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DLMF:7.2.E2
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    Statements

    DLMF defining formula
    erfc ⁡ z = 2 π ⁢ ∫ z ∞ e - t 2 ⁢ d t = 1 - erf ⁡ z , complementary-error-function 𝑧 2 𝜋 superscript subscript 𝑧 superscript 𝑒 superscript 𝑡 2 𝑡 1 error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}z=\frac{2}{\sqrt{\pi}}\int_{z}^% {\infty}e^{-t^{2}}\mathrm{d}t=1-\operatorname{erf}z,}}
    0 references
    Symbols used
    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
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    error function
    DLMF 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
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1adec
    0 references

    Identifiers

     
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