DLMF:19.26.E22 (Q6579): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(7 intermediate revisions by the same user not shown)
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.m2aedec
Property / Symbols used
 
Property / Symbols used: symmetric elliptic integral of third kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of third kind / qualifier
 
test:

R J ⁡ ( x , y , z , p ) Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 {\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}

\CarlsonsymellintRJ@{\NVar{x}}{\NVar{y}}{\NVar{z}}{\NVar{p}}
Property / Symbols used: symmetric elliptic integral of third kind / qualifier
 
xml-id: C19.S16.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11876 / rank
 
Normal rank
Property / Symbols used: Q11876 / qualifier
 
test:

λ 𝜆 {\displaystyle{\displaystyle\lambda}}

\lambda
Property / Symbols used: Q11876 / qualifier
 
xml-id: C19.S26.XMD1.m1pdec
Property / Symbols used
 
Property / Symbols used: Q11886 / rank
 
Normal rank
Property / Symbols used: Q11886 / qualifier
 
test:

α 𝛼 {\displaystyle{\displaystyle\alpha}}

\alpha
Property / Symbols used: Q11886 / qualifier
 
xml-id: C19.S26.XMD11.m1dec
Property / Symbols used
 
Property / Symbols used: Q11887 / rank
 
Normal rank
Property / Symbols used: Q11887 / qualifier
 
test:

β 𝛽 {\displaystyle{\displaystyle\beta}}

\beta
Property / Symbols used: Q11887 / qualifier
 
xml-id: C19.S26.XMD12.m1dec
Property / Symbols used
 
Property / Symbols used: Q11877 / rank
 
Normal rank
Property / Symbols used: Q11877 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11877 / qualifier
 
xml-id: C19.S26.XMD2.m1qdec
Property / Symbols used
 
Property / Symbols used: Q11878 / rank
 
Normal rank
Property / Symbols used: Q11878 / qualifier
 
test:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11878 / qualifier
 
xml-id: C19.S26.XMD3.m1rdec
Property / Symbols used
 
Property / Symbols used: Q11879 / rank
 
Normal rank
Property / Symbols used: Q11879 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11879 / qualifier
 
xml-id: C19.S26.XMD4.m1odec

Latest revision as of 13:14, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:19.26.E22
No description defined

    Statements

    test
    R J ⁡ ( x , y , z , p ) = 2 ⁢ R J ⁡ ( x + λ , y + λ , z + λ , p + λ ) + 3 ⁢ R C ⁡ ( α 2 , β 2 ) , Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 2 Carlson-integral-RJ 𝑥 𝜆 𝑦 𝜆 𝑧 𝜆 𝑝 𝜆 3 Carlson-integral-RC superscript 𝛼 2 superscript 𝛽 2 {\displaystyle{\displaystyle R_{J}\left(x,y,z,p\right)=2R_{J}\left(x+\lambda,y% +\lambda,z+\lambda,p+\lambda\right)+3R_{C}\left(\alpha^{2},\beta^{2}\right),}}
    0 references
    DLMF id
    DLMF:19.26.E22
    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.m2aedec
    0 references
    symmetric elliptic integral of third kind
    test
    R J ⁡ ( x , y , z , p ) Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 {\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}
    xml-id
    C19.S16.E2.m2aadec
    0 references
    Q11876
    test
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C19.S26.XMD1.m1pdec
    0 references
    Q11886
    test
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C19.S26.XMD11.m1dec
    0 references
    Q11887
    test
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C19.S26.XMD12.m1dec
    0 references
    Q11877
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C19.S26.XMD2.m1qdec
    0 references
    Q11878
    test
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C19.S26.XMD3.m1rdec
    0 references
    Q11879
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C19.S26.XMD4.m1odec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q6579&oldid=36930"