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Statements
𝖯
-
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i
τ
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cos
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sin
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shorthand-Ferrers-Legendre-P-first-kind
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𝑖
𝜏
𝜃
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4
superscript
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superscript
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superscript
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{\displaystyle{\displaystyle\mathsf{P}_{-\frac{1}{2}+i\tau}\left(\cos\theta%
\right)=1+\frac{4\tau^{2}+1^{2}}{2^{2}}{\sin^{2}}\left(\tfrac{1}{2}\theta%
\right)+\frac{\left(4\tau^{2}+1^{2}\right)\left(4\tau^{2}+3^{2}\right)}{2^{2}%
\cdot 4^{2}}{\sin^{4}}\left(\tfrac{1}{2}\theta\right)+\cdots,}}
0
≤
θ
≤
π
0
𝜃
𝜋
{\displaystyle{\displaystyle 0\leq\theta\leq\pi}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
𝖯
ν
(
x
)
=
𝖯
ν
0
(
x
)
shorthand-Ferrers-Legendre-P-first-kind
𝜈
𝑥
Ferrers-Legendre-P-first-kind
0
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=%
\mathsf{P}^{0}_{\nu}\left(x\right)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
τ
𝜏
{\displaystyle{\displaystyle\tau}}
