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Statements
𝒲
{
𝖯
-
1
2
+
i
τ
-
μ
(
x
)
,
𝖰
^
-
1
2
+
i
τ
-
μ
(
x
)
}
=
π
(
e
-
τ
π
cos
2
(
μ
π
)
+
sinh
(
τ
π
)
)
|
Γ
(
μ
+
1
2
+
i
τ
)
|
2
(
cosh
2
(
τ
π
)
-
sin
2
(
μ
π
)
)
(
1
-
x
2
)
,
Wronskian
Ferrers-Legendre-P-first-kind
𝜇
1
2
imaginary-unit
𝜏
𝑥
Ferrers-conical-legendre-Q-hat
𝜇
1
2
imaginary-unit
𝜏
𝑥
𝜋
superscript
𝑒
𝜏
𝜋
2
𝜇
𝜋
𝜏
𝜋
superscript
Euler-Gamma
𝜇
1
2
imaginary-unit
𝜏
2
2
𝜏
𝜋
2
𝜇
𝜋
1
superscript
𝑥
2
{\displaystyle{\displaystyle\mathscr{W}\left\{\mathsf{P}^{-\mu}_{-\frac{1}{2}+%
\mathrm{i}\tau}\left(x\right),\widehat{\mathsf{Q}}^{-\mu}_{-\frac{1}{2}+%
\mathrm{i}\tau}\left(x\right)\right\}=\frac{\pi(e^{-\tau\pi}{\cos^{2}}\left(%
\mu\pi\right)+\sinh\left(\tau\pi\right))}{|\Gamma\left(\mu+\frac{1}{2}+\mathrm%
{i}\tau\right)|^{2}({\cosh^{2}}\left(\tau\pi\right)-{\sin^{2}}\left(\mu\pi%
\right))(1-x^{2})},}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\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)}}
𝖰
^
-
1
2
+
i
τ
-
μ
(
x
)
Ferrers-conical-legendre-Q-hat
𝜇
1
2
𝑖
𝜏
𝑥
{\displaystyle{\displaystyle\widehat{\mathsf{Q}}^{-\NVar{\mu}}_{\NVar{-\frac{1%
}{2}+i\tau}}\left(\NVar{x}\right)}}
𝒲
Wronskian
{\displaystyle{\displaystyle\mathscr{W}}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
cosh
z
𝑧
{\displaystyle{\displaystyle\cosh\NVar{z}}}
sinh
z
𝑧
{\displaystyle{\displaystyle\sinh\NVar{z}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
τ
𝜏
{\displaystyle{\displaystyle\tau}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
