Formula:3275

Digital Library of Mathematical Functions ID 8.11.E6

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

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{\pi}{2}-\delta}}$
${\displaystyle{\displaystyle 0<\lambda<1}}$
${\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{\pi}{2}-\delta}}$

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
 

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