DLMF:14.5.E26 (Q4738)

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Language	Label	Description	Also known as
English	DLMF:14.5.E26	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\boldsymbol{Q}_{\frac{1}{2}}\left(\cosh\xi\right)=% 2\pi^{-1/2}\cosh\xi\operatorname{sech}\left(\tfrac{1}{2}\xi\right)K\left(% \operatorname{sech}\left(\tfrac{1}{2}\xi\right)\right)-4\pi^{-1/2}\cosh\left(% \tfrac{1}{2}\xi\right)E\left(\operatorname{sech}\left(\tfrac{1}{2}\xi\right)% \right),}}

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DLMF:14.5.E26

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aodec

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Defining formula

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

C19.S2.E8.m1aedec

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Defining formula

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

C19.S2.E8.m2acdec

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hyperbolic cosine function

Defining formula

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

C4.S28.E2.m2afdec

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hyperbolic secant function

Defining formula

{\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}

C4.S28.E6.m2adec

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Defining formula

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

C14.S2.SS2.p2.m6abdec

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Defining formula

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

C14.S5.XMD1.m1fdec

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Sitelinks

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