DLMF:14.5.E20 (Q4732)

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DLMF:14.5.E20
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    test
    𝖯 1 2 ⁡ ( cos ⁡ θ ) = 2 π ⁢ ( 2 ⁢ E ⁡ ( sin ⁡ ( 1 2 ⁢ θ ) ) - K ⁡ ( sin ⁡ ( 1 2 ⁢ θ ) ) ) , shorthand-Ferrers-Legendre-P-first-kind 1 2 𝜃 2 𝜋 2 complete-elliptic-integral-second-kind-E 1 2 𝜃 complete-elliptic-integral-first-kind-K 1 2 𝜃 {\displaystyle{\displaystyle\mathsf{P}_{\frac{1}{2}}\left(\cos\theta\right)=% \frac{2}{\pi}\left(2E\left(\sin\left(\tfrac{1}{2}\theta\right)\right)-K\left(% \sin\left(\tfrac{1}{2}\theta\right)\right)\right),}}
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    DLMF id
    DLMF:14.5.E20
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