DLMF:7.18.E4 (Q2454)

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DLMF:7.18.E4
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    Statements

    Defining formula
    d n d z n ⁡ ( e z 2 ⁢ erfc ⁡ z ) = ( - 1 ) n ⁢ 2 n ⁢ n ! ⁢ e z 2 ⁢ i n ⁢ erfc ⁡ ( z ) , derivative 𝑧 𝑛 superscript 𝑒 superscript 𝑧 2 complementary-error-function 𝑧 superscript 1 𝑛 superscript 2 𝑛 𝑛 superscript 𝑒 superscript 𝑧 2 repeated-integral-complementary-error-function 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {z^{2}}\operatorname{erfc}z\right)=(-1)^{n}2^{n}n!e^{z^{2}}\mathop{\mathrm{i}^% {n}\mathrm{erfc}}\left(z\right),}}
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    DLMF id
    DLMF:7.18.E4
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    constraint
    n = 0 , 1 , 2 , … 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\dots}}
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    Symbols used
    complementary error function
    Defining formula
    erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    xml-id
    C7.S2.E2.m2aadec
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    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2aadec
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