DLMF:7.18.E6 (Q2456)

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DLMF:7.18.E6
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    Statements

    Defining formula
    i n ⁢ erfc ⁡ ( z ) = ∑ k = 0 ∞ ( - 1 ) k ⁢ z k 2 n - k ⁢ k ! ⁢ Γ ⁡ ( 1 + 1 2 ⁢ ( n - k ) ) . repeated-integral-complementary-error-function 𝑛 𝑧 superscript subscript 𝑘 0 superscript 1 𝑘 superscript 𝑧 𝑘 superscript 2 𝑛 𝑘 𝑘 Euler-Gamma 1 1 2 𝑛 𝑘 {\displaystyle{\displaystyle\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z\right)% =\sum_{k=0}^{\infty}\frac{(-1)^{k}z^{k}}{2^{n-k}k!\Gamma\left(1+\frac{1}{2}(n-% k)\right)}.}}
    0 references
    DLMF id
    DLMF:7.18.E6
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
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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.m2afdec
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    Q11312
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1edec
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    Q11314
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C7.S1.XMD3.m1edec
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