DLMF:19.6.E8 (Q6158)

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Language	Label	Description	Also known as
English	DLMF:19.6.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle F\left(\phi,1\right)=(\sin\phi)R_{C}\left(1,{\cos% ^{2}}\phi\right)={\operatorname{gd}^{-1}}\left(\phi\right).}}

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DLMF:19.6.E8

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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.m2adec

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cosine function

Defining formula

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

C4.S14.E2.m2adec

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Legendre’s incomplete elliptic integral of the first kind

Defining formula

{\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}

C19.S2.E4.m2aadec

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inverse Gudermannian function

Defining formula

{\displaystyle{\displaystyle{\operatorname{gd}^{-1}}\left(\NVar{x}\right)}}

C4.S23.E41.m2adec

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Defining formula

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

C4.S14.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle\phi}}

C19.S1.XMD4.m1adec

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