DLMF:7.18.E13 (Q2463)

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DLMF:7.18.E13
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    Statements

    Defining formula
    i n ⁢ erfc ⁡ ( z ) i n - 1 ⁢ erfc ⁡ ( z ) = 1 / 2 z + ( n + 1 ) / 2 z + ( n + 2 ) / 2 z + ⁢ ⋯ , repeated-integral-complementary-error-function 𝑛 𝑧 repeated-integral-complementary-error-function 𝑛 1 𝑧 continued-fraction 1 2 𝑧 continued-fraction 𝑛 1 2 𝑧 continued-fraction 𝑛 2 2 limit-from 𝑧 ⋯ {\displaystyle{\displaystyle\frac{\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z% \right)}{\mathop{\mathrm{i}^{n-1}\mathrm{erfc}}\left(z\right)}=\cfrac{1/2}{z+% \cfrac{(n+1)/2}{z+\cfrac{(n+2)/2}{z+}}}\cdots,}}
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    DLMF id
    DLMF:7.18.E13
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    constraint
    ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
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    Symbols used
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.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.m2amdec
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