DLMF:19.2.E20 (Q6116)

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Language	Label	Description	Also known as
English	DLMF:19.2.E20	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle R_{C}\left(x,y\right)=\sqrt{\frac{x}{x-y}}R_{C}% \left(x-y,-y\right)=\frac{1}{\sqrt{x-y}}\operatorname{arctanh}\sqrt{\frac{x}{x% -y}}=\frac{1}{\sqrt{x-y}}\ln\frac{\sqrt{x}+\sqrt{x-y}}{\sqrt{-y}},}}

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DLMF:19.2.E20

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{\displaystyle{\displaystyle y<0\leq x}}

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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.m2acdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}

C4.S37.SS2.p1.m10aadec

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principal branch of logarithm function

Defining formula

{\displaystyle{\displaystyle\ln\NVar{z}}}

C4.S2.E2.m2aadec

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