DLMF:14.5.E24 (Q4736)

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Language	Label	Description	Also known as
English	DLMF:14.5.E24	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle P_{\frac{1}{2}}\left(\cosh\xi\right)=\frac{2}{\pi% }e^{\xi/2}E\left(\left(1-e^{-2\xi}\right)^{1/2}\right),}}

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DLMF:14.5.E24

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2amdec

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Defining formula

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

C19.S2.E8.m2abdec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2adec

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hyperbolic cosine function

Defining formula

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

C4.S28.E2.m2addec

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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.m3abdec

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Defining formula

{\displaystyle{\displaystyle\xi>0}}

C14.S5.XMD1.m1ddec

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