DLMF:7.18.E11 (Q2461)

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DLMF:7.18.E11
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    Statements

    Defining formula
    i n ⁢ erfc ⁡ ( z ) = e - z 2 / 2 2 n - 1 ⁢ π ⁢ U ⁡ ( n + 1 2 , z ⁢ 2 ) . repeated-integral-complementary-error-function 𝑛 𝑧 superscript 𝑒 superscript 𝑧 2 2 superscript 2 𝑛 1 𝜋 parabolic-U 𝑛 1 2 𝑧 2 {\displaystyle{\displaystyle\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z\right)% =\frac{e^{-z^{2}/2}}{\sqrt{2^{n-1}\pi}}U\left(n+\tfrac{1}{2},z\sqrt{2}\right).}}
    0 references
    DLMF id
    DLMF:7.18.E11
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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.m2acdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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    Q11320
    Defining formula
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1adec
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    repeated integrals of the complementary error function
    Defining formula
    i n ⁢ erfc ⁡ ( z ) repeated-integral-complementary-error-function 𝑛 𝑧 {\displaystyle{\displaystyle\mathop{\mathrm{i}^{\NVar{n}}\mathrm{erfc}}\left(% \NVar{z}\right)}}
    xml-id
    C7.S18.E2.m2akdec
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    Q11312
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1jdec
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    Q11314
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C7.S1.XMD3.m1jdec
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