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DLMF:10.21.E18 - MaRDI portal
Statements
d
c
′
d
ν
=
2
c
′
c
′
2
-
ν
2
∫
0
∞
(
c
′
2
cosh
(
2
t
)
-
ν
2
)
K
0
(
2
c
′
sinh
t
)
e
-
2
ν
t
d
t
,
derivative
superscript
𝑐
′
𝜈
2
superscript
𝑐
′
superscript
superscript
𝑐
′
2
superscript
𝜈
2
superscript
subscript
0
superscript
superscript
𝑐
′
2
2
𝑡
superscript
𝜈
2
modified-Bessel-second-kind
0
2
superscript
𝑐
′
𝑡
superscript
𝑒
2
𝜈
𝑡
𝑡
{\displaystyle{\displaystyle\frac{\mathrm{d}c^{\prime}}{\mathrm{d}\nu}=\frac{2%
c^{\prime}}{{c^{\prime}}^{2}-\nu^{2}}\*\int_{0}^{\infty}({c^{\prime}}^{2}\cosh%
\left(2t\right)-\nu^{2})\*K_{0}\left(2c^{\prime}\sinh t\right)e^{-2\nu t}%
\mathrm{d}t,}}
d
f
d
x
derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
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)}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
c
𝑐
{\displaystyle{\displaystyle c}}
Identifiers