DLMF:13.9.E9

MaRDI QIDQ5149

• Label: DLMF:13.9.E9

Digital Library of Mathematical Functions ID 13.9.E9

${\displaystyle{\displaystyle z=\pm(2n+a)\pi\mathrm{i}+\ln\left(-\frac{\Gamma\left(a\right)}{\Gamma\left(b-a\right)}\left(\pm 2n\pi\mathrm{i}\right)^{b-2a}\right)+O\left(n^{-1}\ln n\right),}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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