DLMF:1.10.E7 (Q332): Difference between revisions

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DLMF:1.10.E7
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    Statements

    DLMF defining formula
    a n = 1 2 ⁢ π ⁢ i ⁢ ∫ | z - z 0 | = r f ⁢ ( z ) ( z - z 0 ) n + 1 ⁢ d z , subscript 𝑎 𝑛 1 2 𝜋 𝑖 subscript 𝑧 subscript 𝑧 0 𝑟 𝑓 𝑧 superscript 𝑧 subscript 𝑧 0 𝑛 1 𝑧 {\displaystyle{\displaystyle a_{n}=\frac{1}{2\pi i}\int_{|z-z_{0}|=r}\frac{f(z% )}{(z-z_{0})^{n+1}}\mathrm{d}z,}}
    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.m2adec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1edec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1bdec
    0 references
    annulus radii
    DLMF defining formula
    r 1 subscript 𝑟 1 {\displaystyle{\displaystyle r_{1}}}
    xml-id
    C1.S10.XMD4.m1dec
    0 references

    Identifiers

     
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