DLMF:1.9.E33 (Q308)

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DLMF:1.9.E33
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    Statements

    Defining formula
    u ⁢ ( z ) = 1 2 ⁢ π ⁢ ∫ 0 2 ⁢ π u ⁢ ( z + r ⁢ e i ⁢ ϕ ) ⁢ d ϕ . 𝑢 𝑧 1 2 𝜋 subscript superscript 2 𝜋 0 𝑢 𝑧 𝑟 superscript 𝑒 𝑖 italic-ϕ italic-ϕ {\displaystyle{\displaystyle u(z)=\frac{1}{2\pi}\int^{2\pi}_{0}u(z+re^{i\phi})% \mathrm{d}\phi.}}
    0 references
    DLMF id
    DLMF:1.9.E33
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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