DLMF:19.2.E20 (Q6116): Difference between revisions

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

y<0\leq x
Property / constraint: y < 0 x 𝑦 0 𝑥 {\displaystyle{\displaystyle y<0\leq x}} / rank
 
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Revision as of 18:04, 30 December 2019

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DLMF:19.2.E20
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    R C ( x , y ) = x x - y R C ( x - y , - y ) = 1 x - y arctanh x x - y = 1 x - y ln x + x - y - y , Carlson-integral-RC 𝑥 𝑦 𝑥 𝑥 𝑦 Carlson-integral-RC 𝑥 𝑦 𝑦 1 𝑥 𝑦 hyperbolic-inverse-tangent 𝑥 𝑥 𝑦 1 𝑥 𝑦 𝑥 𝑥 𝑦 𝑦 {\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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    y < 0 x 𝑦 0 𝑥 {\displaystyle{\displaystyle y<0\leq x}}
    0 references