DLMF:19.26.E8 (Q6560): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11876 / rank
 
Normal rank
Property / Symbols used: Q11876 / qualifier
 
Defining formula:

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

\lambda
Property / Symbols used: Q11876 / qualifier
 
xml-id: C19.S26.XMD1.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11877 / rank
 
Normal rank
Property / Symbols used: Q11877 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11877 / qualifier
 
xml-id: C19.S26.XMD2.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11878 / rank
 
Normal rank
Property / Symbols used: Q11878 / qualifier
 
Defining formula:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11878 / qualifier
 
xml-id: C19.S26.XMD3.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11879 / rank
 
Normal rank
Property / Symbols used: Q11879 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11879 / qualifier
 
xml-id: C19.S26.XMD4.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11880 / rank
 
Normal rank
Property / Symbols used: Q11880 / qualifier
 
Defining formula:

μ > 0 𝜇 0 {\displaystyle{\displaystyle\mu>0}}

\mu>0
Property / Symbols used: Q11880 / qualifier
 
xml-id: C19.S26.XMD5.m1fdec

Latest revision as of 14:12, 2 January 2020

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DLMF:19.26.E8
No description defined

    Statements

    Defining formula
    2 ⁢ R G ⁡ ( x + λ , y + λ , z + λ ) + 2 ⁢ R G ⁡ ( x + μ , y + μ , z + μ ) = 2 ⁢ R G ⁡ ( x , y , z ) + λ ⁢ R F ⁡ ( x + λ , y + λ , z + λ ) + μ ⁢ R F ⁡ ( x + μ , y + μ , z + μ ) + λ + μ + x + y + z . 2 Carlson-integral-RG 𝑥 𝜆 𝑦 𝜆 𝑧 𝜆 2 Carlson-integral-RG 𝑥 𝜇 𝑦 𝜇 𝑧 𝜇 2 Carlson-integral-RG 𝑥 𝑦 𝑧 𝜆 Carlson-integral-RF 𝑥 𝜆 𝑦 𝜆 𝑧 𝜆 𝜇 Carlson-integral-RF 𝑥 𝜇 𝑦 𝜇 𝑧 𝜇 𝜆 𝜇 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle 2R_{G}\left(x+\lambda,y+\lambda,z+\lambda\right)+% 2R_{G}\left(x+\mu,y+\mu,z+\mu\right)=2R_{G}\left(x,y,z\right)+\lambda R_{F}% \left(x+\lambda,y+\lambda,z+\lambda\right)+\mu R_{F}\left(x+\mu,y+\mu,z+\mu% \right)+\sqrt{\lambda+\mu+x+y+z}.}}
    0 references
    DLMF id
    DLMF:19.26.E8
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    Defining formula
    R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.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.m2adec
    0 references
    Q11876
    Defining formula
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C19.S26.XMD1.m1fdec
    0 references
    Q11877
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C19.S26.XMD2.m1fdec
    0 references
    Q11878
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C19.S26.XMD3.m1fdec
    0 references
    Q11879
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C19.S26.XMD4.m1gdec
    0 references
    Q11880
    Defining formula
    μ > 0 𝜇 0 {\displaystyle{\displaystyle\mu>0}}
    xml-id
    C19.S26.XMD5.m1fdec
    0 references
     
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