DLMF:19.2.E19 (Q6115)

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DLMF:19.2.E19
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    R C ( x , y ) = 1 x - y arctanh x - y x = 1 x - y ln x + x - y y , Carlson-integral-RC 𝑥 𝑦 1 𝑥 𝑦 hyperbolic-inverse-tangent 𝑥 𝑦 𝑥 1 𝑥 𝑦 𝑥 𝑥 𝑦 𝑦 {\displaystyle{\displaystyle R_{C}\left(x,y\right)=\frac{1}{\sqrt{x-y}}% \operatorname{arctanh}\sqrt{\frac{x-y}{x}}=\frac{1}{\sqrt{x-y}}\ln\frac{\sqrt{% x}+\sqrt{x-y}}{\sqrt{y}},}}
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    DLMF:19.2.E19
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