Formula:6812

Digital Library of Mathematical Functions ID 19.2.E20

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \CarlsonellintRC@{x}{y}=\sqrt{\frac{x}{x-y}}\CarlsonellintRC@{x-y}{-y}=\frac{1}{\sqrt{x-y}}\atanh@@{\sqrt{\frac{x}{x-y}}}=\frac{1}{\sqrt{x-y}}\ln@@{\frac{\sqrt{x}+\sqrt{x-y}}{\sqrt{-y}}},}

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}$: Carlson’s combination of inverse circular and inverse hyperbolic functions
• ${\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
 

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