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DLMF:14.23.E7 - MaRDI portal
Statements
𝖰
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π
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Q
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.
Ferrers-conical-legendre-Q-hat
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𝑖
𝜏
𝑥
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superscript
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3
𝜇
𝜋
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Legendre-Q-second-kind
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𝜏
𝑥
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0
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superscript
𝑒
3
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Legendre-Q-second-kind
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2
𝑖
𝜏
𝑥
𝑖
0
{\displaystyle{\displaystyle\widehat{\mathsf{Q}}^{-\mu}_{-\frac{1}{2}+i\tau}%
\left(x\right)=\tfrac{1}{2}e^{3\mu\pi i/2}Q^{-\mu}_{-\frac{1}{2}+i\tau}\left(x%
-i0\right)+\tfrac{1}{2}e^{-3\mu\pi i/2}Q^{-\mu}_{-\frac{1}{2}-i\tau}\left(x+i0%
\right).}}
𝖰
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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)}}
Q
ν
μ
(
z
)
Legendre-Q-second-kind
𝜇
𝜈
𝑧
{\displaystyle{\displaystyle Q^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
x
𝑥
{\displaystyle{\displaystyle x}}
τ
𝜏
{\displaystyle{\displaystyle\tau}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
Identifiers