DLMF:19.26.E20 (Q6577): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: elliptic integral symmetric in only two variables / rank
 
Normal rank
Property / Symbols used: elliptic integral symmetric in only two variables / qualifier
 
Defining formula:

R D ( x , y , z ) Carlson-integral-RD 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}

\CarlsonsymellintRD@{\NVar{x}}{\NVar{y}}{\NVar{z}}
Property / Symbols used: elliptic integral symmetric in only two variables / qualifier
 
xml-id: C19.S16.E5.m2aadec
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.m1ndec
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.m1odec
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.m1pdec
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.m1mdec

Latest revision as of 14:13, 2 January 2020

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DLMF:19.26.E20
No description defined

    Statements

    R D ( x , y , z ) = 2 R D ( x + λ , y + λ , z + λ ) + 3 z ( z + λ ) . Carlson-integral-RD 𝑥 𝑦 𝑧 2 Carlson-integral-RD 𝑥 𝜆 𝑦 𝜆 𝑧 𝜆 3 𝑧 𝑧 𝜆 {\displaystyle{\displaystyle R_{D}\left(x,y,z\right)=2R_{D}\left(x+\lambda,y+% \lambda,z+\lambda\right)+\frac{3}{\sqrt{z}(z+\lambda)}.}}
    0 references
    DLMF:19.26.E20
    0 references
    R D ( x , y , z ) Carlson-integral-RD 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    C19.S16.E5.m2aadec
    0 references
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    C19.S26.XMD1.m1ndec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C19.S26.XMD2.m1odec
    0 references
    y 𝑦 {\displaystyle{\displaystyle y}}
    C19.S26.XMD3.m1pdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C19.S26.XMD4.m1mdec
    0 references