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Statements
𝖯
-
1
2
+
i
τ
-
μ
(
x
)
=
σ
(
μ
,
τ
)
(
α
2
+
η
1
+
α
2
-
x
2
)
1
/
4
I
μ
(
τ
η
1
/
2
)
(
1
+
O
(
1
/
τ
)
)
,
Ferrers-Legendre-P-first-kind
𝜇
1
2
𝑖
𝜏
𝑥
𝜎
𝜇
𝜏
superscript
superscript
𝛼
2
𝜂
1
superscript
𝛼
2
superscript
𝑥
2
1
4
modified-Bessel-first-kind
𝜇
𝜏
superscript
𝜂
1
2
1
Big-O
1
𝜏
{\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{-\frac{1}{2}+i\tau}\left(x%
\right)=\sigma(\mu,\tau)\left(\frac{\alpha^{2}+\eta}{1+\alpha^{2}-x^{2}}\right%
)^{1/4}I_{\mu}\left(\tau\eta^{1/2}\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)}}
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)}}
x
𝑥
{\displaystyle{\displaystyle x}}
τ
𝜏
{\displaystyle{\displaystyle\tau}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
σ
(
μ
,
τ
)
𝜎
𝜇
𝜏
{\displaystyle{\displaystyle\sigma(\mu,\tau)}}
η
𝜂
{\displaystyle{\displaystyle\eta}}
Identifiers
