DLMF:19.20.E5 (Q6382): 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
 
Defining formula:

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: symmetric elliptic integral of second kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of second kind / qualifier
 
Defining formula:

R G ⁡ ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}

\CarlsonsymellintRG@{\NVar{x}}{\NVar{y}}{\NVar{z}}
Property / Symbols used: symmetric elliptic integral of second kind / qualifier
 
xml-id: C19.S16.E3.m2aadec

Latest revision as of 13:57, 2 January 2020

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DLMF:19.20.E5
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    Statements

    Defining formula
    2 ⁢ R G ⁡ ( x , y , y ) = y ⁢ R C ⁡ ( x , y ) + x . 2 Carlson-integral-RG 𝑥 𝑦 𝑦 𝑦 Carlson-integral-RC 𝑥 𝑦 𝑥 {\displaystyle{\displaystyle 2R_{G}\left(x,y,y\right)=yR_{C}\left(x,y\right)+% \sqrt{x}.}}
    0 references
    DLMF id
    DLMF:19.20.E5
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    Defining formula
    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
    symmetric elliptic integral of second kind
    Defining formula
    R G ⁡ ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E3.m2aadec
    0 references
     
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