Formula:3276

Digital Library of Mathematical Functions ID 8.11.E7

${\displaystyle{\displaystyle\Gamma\left(a,z\right)\sim z^{a}e^{-z}\sum_{k=0}^{\infty}\frac{(-a)^{k}b_{k}(\lambda)}{(z-a)^{2k+1}},}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{3\pi}{2}-\delta}}$
${\displaystyle{\displaystyle\lambda>1}}$
${\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{3\pi}{2}-\delta}}$

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
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: parameter
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle\delta}}$: small positive constant
• ${\displaystyle{\displaystyle\lambda}}$: parameter
• ${\displaystyle{\displaystyle b_{k}(\lambda)}}$: coefficients
 

Resources that cite this formula

No records found.