Formula:3274

Digital Library of Mathematical Functions ID 8.11.E5

${\displaystyle{\displaystyle P\left(a,z\right)\sim\frac{z^{a}e^{-z}}{\Gamma\left(1+a\right)}\sim(2\pi a)^{-\frac{1}{2}}e^{a-z}(z/a)^{a},}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}a|\leq\pi-\delta}}$
${\displaystyle{\displaystyle a\to\infty}}$
${\displaystyle{\displaystyle|\operatorname{ph}a|\leq\pi-\delta}}$

Symbols List

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

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