DLMF:13.9.E9 (Q4452)

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DLMF:13.9.E9
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    Statements

    Defining formula
    z = ± ( 2 ⁢ n + a ) ⁢ π ⁢ i + ln ⁡ ( - Γ ⁡ ( a ) Γ ⁡ ( b - a ) ⁢ ( ± 2 ⁢ n ⁢ π ⁢ i ) b - 2 ⁢ a ) + O ⁡ ( n - 1 ⁢ ln ⁡ n ) , 𝑧 plus-or-minus 2 𝑛 𝑎 𝜋 imaginary-unit Euler-Gamma 𝑎 Euler-Gamma 𝑏 𝑎 superscript plus-or-minus 2 𝑛 𝜋 imaginary-unit 𝑏 2 𝑎 Big-O superscript 𝑛 1 𝑛 {\displaystyle{\displaystyle z=\pm(2n+a)\pi\mathrm{i}+\ln\left(-\frac{\Gamma% \left(a\right)}{\Gamma\left(b-a\right)}\left(\pm 2n\pi\mathrm{i}\right)^{b-2a}% \right)+O\left(n^{-1}\ln n\right),}}
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    DLMF id
    DLMF:13.9.E9
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