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Statements
𝖰
^
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1
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+
i
τ
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μ
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x
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=
π
e
-
τ
π
sin
(
μ
π
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sinh
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τ
π
)
2
(
cosh
2
(
τ
π
)
-
sin
2
(
μ
π
)
)
𝖯
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1
2
+
i
τ
-
μ
(
x
)
+
π
(
e
-
τ
π
cos
2
(
μ
π
)
+
sinh
(
τ
π
)
)
2
(
cosh
2
(
τ
π
)
-
sin
2
(
μ
π
)
)
𝖯
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1
2
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i
τ
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μ
(
-
x
)
.
Ferrers-conical-legendre-Q-hat
𝜇
1
2
imaginary-unit
𝜏
𝑥
𝜋
superscript
𝑒
𝜏
𝜋
𝜇
𝜋
𝜏
𝜋
2
2
𝜏
𝜋
2
𝜇
𝜋
Ferrers-Legendre-P-first-kind
𝜇
1
2
imaginary-unit
𝜏
𝑥
𝜋
superscript
𝑒
𝜏
𝜋
2
𝜇
𝜋
𝜏
𝜋
2
2
𝜏
𝜋
2
𝜇
𝜋
Ferrers-Legendre-P-first-kind
𝜇
1
2
imaginary-unit
𝜏
𝑥
{\displaystyle{\displaystyle\widehat{\mathsf{Q}}^{-\mu}_{-\frac{1}{2}+\mathrm{%
i}\tau}\left(x\right)=\frac{\pi e^{-\tau\pi}\sin\left(\mu\pi\right)\sinh\left(%
\tau\pi\right)}{2({\cosh^{2}}\left(\tau\pi\right)-{\sin^{2}}\left(\mu\pi\right%
))}\mathsf{P}^{-\mu}_{-\frac{1}{2}+\mathrm{i}\tau}\left(x\right)+\frac{\pi(e^{%
-\tau\pi}{\cos^{2}}\left(\mu\pi\right)+\sinh\left(\tau\pi\right))}{2({\cosh^{2%
}}\left(\tau\pi\right)-{\sin^{2}}\left(\mu\pi\right))}\mathsf{P}^{-\mu}_{-%
\frac{1}{2}+\mathrm{i}\tau}\left(-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)}}
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)}}
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}}
Identifiers
