DLMF:19.2.E18 (Q6114): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Carlson’s combination of inverse circular and inverse hyperbolic functions / rank
 
Normal rank
Property / Symbols used: Carlson’s combination of inverse circular and inverse hyperbolic functions / qualifier
 
test:

R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}

\CarlsonellintRC@{\NVar{x}}{\NVar{y}}
Property / Symbols used: Carlson’s combination of inverse circular and inverse hyperbolic functions / qualifier
 
xml-id: C19.S2.E17.m2aadec

Revision as of 12:36, 2 January 2020

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DLMF:19.2.E18
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    Statements

    test
    R C ⁡ ( x , y ) = 1 y - x ⁢ arctan ⁡ y - x x = 1 y - x ⁢ arccos ⁡ x / y , Carlson-integral-RC 𝑥 𝑦 1 𝑦 𝑥 𝑦 𝑥 𝑥 1 𝑦 𝑥 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(x,y\right)=\frac{1}{\sqrt{y-x}}% \operatorname{arctan}\sqrt{\frac{y-x}{x}}=\frac{1}{\sqrt{y-x}}\operatorname{% arccos}\sqrt{x/y},}}
    0 references
    DLMF id
    DLMF:19.2.E18
    0 references
    constraint
    0 ≤ x < y 0 𝑥 𝑦 {\displaystyle{\displaystyle 0\leq x<y}}
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    test
    R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2aadec
    0 references
     
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