DLMF:22.16.E33 (Q7153): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Jacobi’s zeta function / rank
 
Normal rank
Property / Symbols used: Jacobi’s zeta function / qualifier
 
test:

Z ⁡ ( x | k ) Jacobi-Zeta 𝑥 𝑘 {\displaystyle{\displaystyle\mathrm{Z}\left(\NVar{x}|\NVar{k}\right)}}

\JacobiZetak@{\NVar{x}}{\NVar{k}}
Property / Symbols used: Jacobi’s zeta function / qualifier
 
xml-id: C22.S16.E32.m2aadec
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
test:

cd ⁡ ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}

\Jacobiellcdk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E8.m2addec
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
test:

sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}

\Jacobiellsnk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E4.m2aldec
Property / Symbols used
 
Property / Symbols used: Q11600 / rank
 
Normal rank
Property / Symbols used: Q11600 / qualifier
 
test:

K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}

\compellintKk@{\NVar{k}}
Property / Symbols used: Q11600 / qualifier
 
xml-id: C19.S2.E8.m1agdec
Property / Symbols used
 
Property / Symbols used: Q12003 / rank
 
Normal rank
Property / Symbols used: Q12003 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12003 / qualifier
 
xml-id: C22.S1.XMD1.m1afdec

Latest revision as of 14:37, 2 January 2020

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DLMF:22.16.E33
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    Statements

    test
    Z ⁡ ( x + K | k ) = Z ⁡ ( x | k ) - k 2 ⁢ sn ⁡ ( x , k ) ⁢ cd ⁡ ( x , k ) , Jacobi-Zeta 𝑥 𝐾 𝑘 Jacobi-Zeta 𝑥 𝑘 superscript 𝑘 2 Jacobi-elliptic-sn 𝑥 𝑘 Jacobi-elliptic-cd 𝑥 𝑘 {\displaystyle{\displaystyle\mathrm{Z}\left(x+K|k\right)=\mathrm{Z}\left(x|k% \right)-k^{2}\operatorname{sn}\left(x,k\right)\operatorname{cd}\left(x,k\right% ),}}
    0 references
    DLMF id
    DLMF:22.16.E33
    0 references
    Symbols used
    Jacobi’s zeta function
    test
    Z ⁡ ( x | k ) Jacobi-Zeta 𝑥 𝑘 {\displaystyle{\displaystyle\mathrm{Z}\left(\NVar{x}|\NVar{k}\right)}}
    xml-id
    C22.S16.E32.m2aadec
    0 references
    Jacobian elliptic function
    test
    cd ⁡ ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m2addec
    0 references
    Jacobian elliptic function
    test
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2aldec
    0 references
    Q11600
    test
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1agdec
    0 references
    Q12003
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1afdec
    0 references
     
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