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DLMF:7.18.E12 - MaRDI portal

DLMF:7.18.E12 (Q3160)

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DLMF:7.18.E12
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    Statements

    DLMF defining formula
    i n ⁢ erfc ⁡ ( z ) = 1 2 n - 1 ⁢ π ⁢ 𝐻ℎ n ⁡ ( 2 ⁢ z ) . repeated-integral-complementary-error-function 𝑛 𝑧 1 superscript 2 𝑛 1 𝜋 Fishers-Hh 𝑛 2 𝑧 {\displaystyle{\displaystyle\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z\right)% =\frac{1}{\sqrt{2^{n-1}\pi}}\mathit{Hh}_{n}\left(\sqrt{2}z\right).}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    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.m2aldec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1kdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C7.S1.XMD3.m1kdec
    0 references

    Identifiers

     
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