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DLMF:7.18.E3 - MaRDI portal

DLMF:7.18.E3 (Q3151)

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DLMF:7.18.E3
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    Statements

    DLMF defining formula
    d d z ⁡ i n ⁢ erfc ⁡ ( z ) = - i n - 1 ⁢ erfc ⁡ ( z ) , derivative 𝑧 repeated-integral-complementary-error-function 𝑛 𝑧 repeated-integral-complementary-error-function 𝑛 1 𝑧 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\mathop{\mathrm{i}^{% n}\mathrm{erfc}}\left(z\right)=-\mathop{\mathrm{i}^{n-1}\mathrm{erfc}}\left(z% \right),}}
    0 references
    constraint
    n = 0 , 1 , 2 , … 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\dots}}
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    Symbols used
    derivative of $$f$$ with respect to $$x$$
    DLMF 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.m2adec
    0 references
    repeated integrals of the complementary error function
    DLMF 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.m2acdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1bdec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C7.S1.XMD3.m1bdec
    0 references

    Identifiers

     
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