DLMF:19.26.E9 (Q6561)

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Language	Label	Description	Also known as
English	DLMF:19.26.E9	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle R_{J}\left(x+\lambda,y+\lambda,z+\lambda,p+% \lambda\right)+R_{J}\left(x+\mu,y+\mu,z+\mu,p+\mu\right)=R_{J}\left(x,y,z,p% \right)-3R_{C}\left(\gamma-\delta,\gamma\right),}}

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DLMF:19.26.E9

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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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symmetric elliptic integral of third kind

Defining formula

{\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}

C19.S16.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle\lambda}}

C19.S26.XMD1.m1gdec

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Defining formula

{\displaystyle{\displaystyle\delta}}

C19.S26.XMD10.m1dec

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Defining formula

{\displaystyle{\displaystyle x}}

C19.S26.XMD2.m1gdec

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Defining formula

{\displaystyle{\displaystyle y}}

C19.S26.XMD3.m1gdec

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Defining formula

{\displaystyle{\displaystyle z}}

C19.S26.XMD4.m1hdec

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Defining formula

{\displaystyle{\displaystyle\mu>0}}

C19.S26.XMD5.m1gdec

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Defining formula

{\displaystyle{\displaystyle\gamma}}

C19.S26.XMD9.m1dec

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