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Statements
𝖯
-
1
2
+
i
τ
-
μ
(
cos
θ
)
=
1
τ
μ
(
θ
sin
θ
)
1
/
2
I
μ
(
τ
θ
)
(
1
+
O
(
1
/
τ
)
)
,
Ferrers-Legendre-P-first-kind
𝜇
1
2
𝑖
𝜏
𝜃
1
superscript
𝜏
𝜇
superscript
𝜃
𝜃
1
2
modified-Bessel-first-kind
𝜇
𝜏
𝜃
1
Big-O
1
𝜏
{\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{-\frac{1}{2}+i\tau}\left(\cos%
\theta\right)=\frac{1}{\tau^{\mu}}\left(\frac{\theta}{\sin\theta}\right)^{1/2}%
I_{\mu}\left(\tau\theta\right)\*\left(1+O\left(\ifrac{1}{\tau}\right)\right),}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
𝖯
ν
μ
(
x
)
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
I
ν
(
z
)
modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
τ
𝜏
{\displaystyle{\displaystyle\tau}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
0
<
θ
<
π
0
𝜃
𝜋
{\displaystyle{\displaystyle 0<\theta<\pi}}
Identifiers
