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
Property / Symbols used
 
Property / Symbols used: Q11208 / rank
 
Normal rank
Property / Symbols used: Q11208 / qualifier
 
test:

arccos z 𝑧 {\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}

\acos@@{\NVar{z}}
Property / Symbols used: Q11208 / qualifier
 
xml-id: C4.S23.SS2.p1.m6adec
Property / Symbols used
 
Property / Symbols used: Q10816 / rank
 
Normal rank
Property / Symbols used: Q10816 / qualifier
 
test:

arctan z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

\atan@@{\NVar{z}}
Property / Symbols used: Q10816 / qualifier
 
xml-id: C4.S23.SS2.p1.m7abdec

Latest revision as of 12:36, 2 January 2020

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DLMF:19.2.E18
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    Statements

    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},}}
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    0 x < y 0 𝑥 𝑦 {\displaystyle{\displaystyle 0\leq x<y}}
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    R C ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    C19.S2.E17.m2aadec
    0 references
    arccos z 𝑧 {\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}
    C4.S23.SS2.p1.m6adec
    0 references
    arctan z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    C4.S23.SS2.p1.m7abdec
    0 references