DLMF:19.25.E30 (Q6538)

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Language	Label	Description	Also known as
English	DLMF:19.25.E30	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{am}\left(u,k\right)=R_{C}\left({% \operatorname{cs}^{2}}\left(u,k\right),{\operatorname{ns}^{2}}\left(u,k\right)% \right),}}

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DLMF:19.25.E30

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Carlson’s combination of inverse circular and inverse hyperbolic functions

Defining formula

{\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}

C19.S2.E17.m2aadec

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Jacobi’s amplitude function

Defining formula

{\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}

C22.S16.E1.m2adec

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Jacobian elliptic function

Defining formula

{\displaystyle{\displaystyle\operatorname{cs}\left(\NVar{z},\NVar{k}\right)}}

C22.S2.E9.m3adec

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Jacobian elliptic function

Defining formula

{\displaystyle{\displaystyle\operatorname{ns}\left(\NVar{z},\NVar{k}\right)}}

C22.S2.E4.m3adec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1acdec

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