DLMF:4.6.E2 (Q1571)

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DLMF:4.6.E2
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    Statements

    Defining formula
    ln ⁡ z = ( z - 1 z ) + 1 2 ⁢ ( z - 1 z ) 2 + 1 3 ⁢ ( z - 1 z ) 3 + ⋯ , 𝑧 𝑧 1 𝑧 1 2 superscript 𝑧 1 𝑧 2 1 3 superscript 𝑧 1 𝑧 3 ⋯ {\displaystyle{\displaystyle\ln z=\left(\frac{z-1}{z}\right)+\frac{1}{2}\left(% \frac{z-1}{z}\right)^{2}+\frac{1}{3}\left(\frac{z-1}{z}\right)^{3}+\cdots,}}
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    DLMF id
    DLMF:4.6.E2
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    constraint
    ℜ ⁡ z ≥ 1 2 𝑧 1 2 {\displaystyle{\displaystyle\Re z\geq\frac{1}{2}}}
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    Symbols used
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
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