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Statements
∫
0
∞
e
-
x
t
q
(
t
)
ln
t
d
t
∼
∑
s
=
0
∞
Γ
′
(
s
+
λ
μ
)
a
s
x
(
s
+
λ
)
/
μ
-
(
ln
x
)
∑
s
=
0
∞
Γ
(
s
+
λ
μ
)
a
s
x
(
s
+
λ
)
/
μ
,
asymptotic-expansion
superscript
subscript
0
superscript
𝑒
𝑥
𝑡
𝑞
𝑡
𝑡
𝑡
superscript
subscript
𝑠
0
diffop
Euler-Gamma
1
𝑠
𝜆
𝜇
subscript
𝑎
𝑠
superscript
𝑥
𝑠
𝜆
𝜇
𝑥
superscript
subscript
𝑠
0
Euler-Gamma
𝑠
𝜆
𝜇
subscript
𝑎
𝑠
superscript
𝑥
𝑠
𝜆
𝜇
{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-xt}q(t)\ln t\mathrm{d}t\sim%
\sum_{s=0}^{\infty}\Gamma'\left(\frac{s+\lambda}{\mu}\right)\frac{a_{s}}{x^{(s%
+\lambda)/\mu}}-(\ln x)\sum_{s=0}^{\infty}\Gamma\left(\frac{s+\lambda}{\mu}%
\right)\frac{a_{s}}{x^{(s+\lambda)/\mu}},}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
∫
{\displaystyle{\displaystyle\int}}
ln
z
𝑧
{\displaystyle{\displaystyle\ln\NVar{z}}}
a
𝑎
{\displaystyle{\displaystyle a}}
q
(
t
)
𝑞
𝑡
{\displaystyle{\displaystyle q(t)}}
λ
𝜆
{\displaystyle{\displaystyle\lambda}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
Identifiers
