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Statements
K
ν
(
x
)
=
sec
(
1
2
ν
π
)
∫
0
∞
cos
(
x
sinh
t
)
cosh
(
ν
t
)
d
t
=
csc
(
1
2
ν
π
)
∫
0
∞
sin
(
x
sinh
t
)
sinh
(
ν
t
)
d
t
,
modified-Bessel-second-kind
𝜈
𝑥
1
2
𝜈
𝜋
superscript
subscript
0
𝑥
𝑡
𝜈
𝑡
𝑡
1
2
𝜈
𝜋
superscript
subscript
0
𝑥
𝑡
𝜈
𝑡
𝑡
{\displaystyle{\displaystyle K_{\nu}\left(x\right)=\sec\left(\tfrac{1}{2}\nu%
\pi\right)\int_{0}^{\infty}\cos\left(x\sinh t\right)\cosh\left(\nu t\right)%
\mathrm{d}t=\csc\left(\tfrac{1}{2}\nu\pi\right)\int_{0}^{\infty}\sin\left(x%
\sinh t\right)\sinh\left(\nu t\right)\mathrm{d}t,}}
|
ℜ
ν
|
<
1
𝜈
1
{\displaystyle{\displaystyle|\Re\nu|<1}}
|
ℜ
ν
|
<
1
𝜈
1
{\displaystyle{\displaystyle|\Re\nu|<1}}
x
>
0
𝑥
0
{\displaystyle{\displaystyle x>0}}
π
{\displaystyle{\displaystyle\pi}}
csc
z
𝑧
{\displaystyle{\displaystyle\csc\NVar{z}}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
cosh
z
𝑧
{\displaystyle{\displaystyle\cosh\NVar{z}}}
sinh
z
𝑧
{\displaystyle{\displaystyle\sinh\NVar{z}}}
∫
{\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}}
sec
z
𝑧
{\displaystyle{\displaystyle\sec\NVar{z}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
