DLMF:19.26.E17 (Q6574): 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.m2addec

Revision as of 13:13, 2 January 2020

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DLMF:19.26.E17
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    Statements

    α R C ( β , α + β ) + β R C ( α , α + β ) = π / 2 , 𝛼 Carlson-integral-RC 𝛽 𝛼 𝛽 𝛽 Carlson-integral-RC 𝛼 𝛼 𝛽 𝜋 2 {\displaystyle{\displaystyle\sqrt{\alpha}R_{C}\left(\beta,\alpha+\beta\right)+% \sqrt{\beta}R_{C}\left(\alpha,\alpha+\beta\right)=\pi/2,}}
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    α , β ( - , 0 ) 𝛼 𝛽 0 {\displaystyle{\displaystyle\alpha,\beta\in\mathbb{C}\setminus(-\infty,0)}}
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    α , β ( - , 0 ) 𝛼 𝛽 0 {\displaystyle{\displaystyle\alpha,\beta\in\mathbb{C}\setminus(-\infty,0)}}
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    α + β > 0 𝛼 𝛽 0 {\displaystyle{\displaystyle\alpha+\beta>0}}
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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.m2addec
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