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Statements
∫
0
x
e
±
t
t
ν
K
ν
(
t
)
d
t
=
e
±
x
x
ν
+
1
2
ν
+
1
(
K
ν
(
x
)
±
K
ν
+
1
(
x
)
)
∓
2
ν
Γ
(
ν
+
1
)
2
ν
+
1
,
superscript
subscript
0
𝑥
superscript
𝑒
plus-or-minus
𝑡
superscript
𝑡
𝜈
modified-Bessel-second-kind
𝜈
𝑡
𝑡
minus-or-plus
superscript
𝑒
plus-or-minus
𝑥
superscript
𝑥
𝜈
1
2
𝜈
1
plus-or-minus
modified-Bessel-second-kind
𝜈
𝑥
modified-Bessel-second-kind
𝜈
1
𝑥
superscript
2
𝜈
Euler-Gamma
𝜈
1
2
𝜈
1
{\displaystyle{\displaystyle\int_{0}^{x}e^{\pm t}t^{\nu}K_{\nu}\left(t\right)%
\mathrm{d}t=\frac{e^{\pm x}x^{\nu+1}}{2\nu+1}(K_{\nu}\left(x\right)\pm K_{\nu+%
1}\left(x\right))\mp\frac{2^{\nu}\Gamma\left(\nu+1\right)}{2\nu+1},}}
ℜ
ν
>
-
1
2
𝜈
1
2
{\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
∫
{\displaystyle{\displaystyle\int}}
K
ν
(
z
)
modified-Bessel-second-kind
𝜈
𝑧
{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
x
𝑥
{\displaystyle{\displaystyle x}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
