Formula:3283

Digital Library of Mathematical Functions ID 8.11.E12

${\displaystyle{\displaystyle\Gamma\left(z,z\right)\sim z^{z-1}e^{-z}\left(\sqrt{\frac{\pi}{2}}z^{\frac{1}{2}}-\frac{1}{3}+\frac{\sqrt{2\pi}}{24z^{\frac{1}{2}}}-\frac{4}{135z}+\frac{\sqrt{2\pi}}{576z^{\frac{3}{2}}}+\frac{8}{2835z^{2}}+\dots\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}z|\leq 2\pi-\delta}}$

Symbols List

• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}$: incomplete gamma function
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\delta}}$: small positive constant
 

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