Formula:2830

Digital Library of Mathematical Functions ID 5.11.E10

${\displaystyle{\displaystyle\Gamma\left(z\right)=e^{-z}z^{z}\left(\frac{2\pi}{z}\right)^{1/2}\left(\sum_{k=0}^{K-1}\frac{g_{k}}{z^{k}}+R_{K}(z)\right),}}$

Constraint(s)

${\displaystyle{\displaystyle K=1,2,3,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle g_{k}}}$: coefficients
• ${\displaystyle{\displaystyle R_{K}(z)}}$: remainder (locally)
 

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