DLMF:14.5.E25 (Q4737)

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Language	Label	Description	Also known as
English	DLMF:14.5.E25	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle P_{-\frac{1}{2}}\left(\cosh\xi\right)=\frac{2}{% \pi\cosh\left(\frac{1}{2}\xi\right)}K\left(\tanh\left(\tfrac{1}{2}\xi\right)% \right),}}

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DLMF:14.5.E25

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2andec

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Defining formula

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

C19.S2.E8.m1addec

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hyperbolic cosine function

Defining formula

{\displaystyle{\displaystyle\cosh\NVar{z}}}

C4.S28.E2.m2aedec

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hyperbolic tangent function

Defining formula

{\displaystyle{\displaystyle\tanh\NVar{z}}}

C4.S28.E4.m2adec

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Defining formula

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

C14.S2.SS2.p2.m3acdec

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Sitelinks

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