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Statements
Y
~
ν
(
x
)
=
(
2
coth
(
1
2
π
ν
)
π
ν
)
1
2
sin
(
ν
ln
(
1
2
x
)
-
γ
ν
)
+
O
(
x
2
)
,
Bessel-Y-Weber-imaginary-order
𝜈
𝑥
superscript
2
hyperbolic-cotangent
1
2
𝜈
𝜈
1
2
𝜈
1
2
𝑥
subscript
𝛾
𝜈
Big-O
superscript
𝑥
2
{\displaystyle{\displaystyle\widetilde{Y}_{\nu}\left(x\right)=\left(\frac{2%
\coth\left(\frac{1}{2}\pi\nu\right)}{\pi\nu}\right)^{\frac{1}{2}}\*\sin\left(%
\nu\ln\left(\tfrac{1}{2}x\right)-\gamma_{\nu}\right)+O\left(x^{2}\right),}}
ν
>
0
𝜈
0
{\displaystyle{\displaystyle\nu>0}}
Y
~
ν
(
x
)
Bessel-Y-Weber-imaginary-order
𝜈
𝑥
{\displaystyle{\displaystyle\widetilde{Y}_{\NVar{\nu}}\left(\NVar{x}\right)}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
π
{\displaystyle{\displaystyle\pi}}
coth
z
hyperbolic-cotangent
𝑧
{\displaystyle{\displaystyle\coth\NVar{z}}}
ln
z
𝑧
{\displaystyle{\displaystyle\ln\NVar{z}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
γ
ν
subscript
𝛾
𝜈
{\displaystyle{\displaystyle\gamma_{\nu}}}
