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Statements
∫
0
∞
e
-
a
t
E
n
(
t
)
d
t
=
(
-
1
)
n
-
1
a
n
(
ln
(
1
+
a
)
+
∑
k
=
1
n
-
1
(
-
1
)
k
a
k
k
)
,
superscript
subscript
0
superscript
𝑒
𝑎
𝑡
exponential-integral-En
𝑛
𝑡
𝑡
superscript
1
𝑛
1
superscript
𝑎
𝑛
1
𝑎
superscript
subscript
𝑘
1
𝑛
1
superscript
1
𝑘
superscript
𝑎
𝑘
𝑘
{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}E_{n}\left(t\right)\mathrm%
{d}t=\frac{(-1)^{n-1}}{a^{n}}\left(\ln\left(1+a\right)+\sum_{k=1}^{n-1}\frac{(%
-1)^{k}a^{k}}{k}\right),}}
ℜ
a
>
-
1
𝑎
1
{\displaystyle{\displaystyle\Re a>-1}}
n
=
1
,
2
,
…
𝑛
1
2
…
{\displaystyle{\displaystyle n=1,2,\dots}}
ℜ
a
>
-
1
𝑎
1
{\displaystyle{\displaystyle\Re a>-1}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
E
p
(
z
)
exponential-integral-En
𝑝
𝑧
{\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}
∫
{\displaystyle{\displaystyle\int}}
ln
z
𝑧
{\displaystyle{\displaystyle\ln\NVar{z}}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
a
𝑎
{\displaystyle{\displaystyle a}}
k
𝑘
{\displaystyle{\displaystyle k}}
n
𝑛
{\displaystyle{\displaystyle n}}
Identifiers
