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Statements
γ
(
a
,
z
)
∼
-
z
a
e
-
z
∑
k
=
0
∞
(
-
a
)
k
b
k
(
λ
)
(
z
-
a
)
2
k
+
1
,
asymptotic-expansion
incomplete-gamma
𝑎
𝑧
superscript
𝑧
𝑎
superscript
𝑒
𝑧
superscript
subscript
𝑘
0
superscript
𝑎
𝑘
subscript
𝑏
𝑘
𝜆
superscript
𝑧
𝑎
2
𝑘
1
{\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}},}}
|
ph
a
|
≤
π
2
-
δ
phase
𝑎
𝜋
2
𝛿
{\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{\pi}{2}-\delta}}
0
<
λ
<
1
0
𝜆
1
{\displaystyle{\displaystyle 0<\lambda<1}}
|
ph
a
|
≤
π
2
-
δ
ph
𝑎
𝜋
2
𝛿
{\displaystyle{\displaystyle|\operatorname{ph}a|\leq\frac{\pi}{2}-\delta}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
γ
(
a
,
z
)
incomplete-gamma
𝑎
𝑧
{\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
x
𝑥
{\displaystyle{\displaystyle x}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
k
𝑘
{\displaystyle{\displaystyle k}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
λ
𝜆
{\displaystyle{\displaystyle\lambda}}
b
k
(
λ
)
subscript
𝑏
𝑘
𝜆
{\displaystyle{\displaystyle b_{k}(\lambda)}}
