DLMF:14.5.E20 (Q4732)

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Language	Label	Description	Also known as
English	DLMF:14.5.E20	No description defined

Statements

Defining formula

{\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:14.5.E20

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2akdec

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Defining formula

{\displaystyle{\displaystyle K\left(\NVar{k}\right)}}

C19.S2.E8.m1adec

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Defining formula

{\displaystyle{\displaystyle E\left(\NVar{k}\right)}}

C19.S2.E8.m2adec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2afdec

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Defining formula

{\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{P}^{0}_{\nu}\left(x\right)}}

C14.S2.SS2.p2.m2abdec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2afdec

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Defining formula

{\displaystyle{\displaystyle 0<\theta<\pi}}

C14.S5.XMD2.m1edec

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Sitelinks

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