DLMF:19.25.E31 (Q6539): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: symmetric elliptic integral of first kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of first kind / qualifier
 
test:

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

\CarlsonsymellintRF@{\NVar{x}}{\NVar{y}}{\NVar{z}}
Property / Symbols used: symmetric elliptic integral of first kind / qualifier
 
xml-id: C19.S16.E1.m2aidec
Property / Symbols used
 
Property / Symbols used: generic Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: generic Jacobian elliptic function / qualifier
 
test:

p ⁣ q ⁡ ( z , k ) abstract-Jacobi-elliptic p q 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{pq}\left(\NVar{z},\NVar{k}\right)}}

\genJacobiellk{p}{q}@{\NVar{z}}{\NVar{k}}
Property / Symbols used: generic Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E10.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11808 / rank
 
Normal rank
Property / Symbols used: Q11808 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11808 / qualifier
 
xml-id: C19.S1.XMD5.m1addec

Latest revision as of 13:09, 2 January 2020

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DLMF:19.25.E31
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    Statements

    test
    u = R F ⁡ ( p ⁣ s 2 ⁡ ( u , k ) , q ⁣ s 2 ⁡ ( u , k ) , r ⁣ s 2 ⁡ ( u , k ) ) ; 𝑢 Carlson-integral-RF abstract-Jacobi-elliptic p s 2 𝑢 𝑘 abstract-Jacobi-elliptic q s 2 𝑢 𝑘 abstract-Jacobi-elliptic r s 2 𝑢 𝑘 {\displaystyle{\displaystyle u=R_{F}\left({\operatorname{ps}^{2}}\left(u,k% \right),{\operatorname{qs}^{2}}\left(u,k\right),{\operatorname{rs}^{2}}\left(u% ,k\right)\right);}}
    0 references
    DLMF id
    DLMF:19.25.E31
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    test
    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.m2aidec
    0 references
    generic Jacobian elliptic function
    test
    p ⁣ q ⁡ ( z , k ) abstract-Jacobi-elliptic p q 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{pq}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E10.m2aadec
    0 references
    Q11808
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1addec
    0 references
     
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