DLMF:22.8.E1 (Q6966): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
test:

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

\Jacobiellcnk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E5.m2adec
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
test:

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

\Jacobielldnk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E6.m2adec
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q11991 / rank
 
Normal rank
Property / Symbols used: Q11991 / qualifier
 
test:

u 𝑢 {\displaystyle{\displaystyle u}}

u
Property / Symbols used: Q11991 / qualifier
 
xml-id: C22.S8.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q11992 / rank
 
Normal rank
Property / Symbols used: Q11992 / qualifier
 
test:

v 𝑣 {\displaystyle{\displaystyle v}}

v
Property / Symbols used: Q11992 / qualifier
 
xml-id: C22.S8.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q11993 / rank
 
Normal rank
Property / Symbols used: Q11993 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11993 / qualifier
 
xml-id: C22.S8.XMD3.m1dec

Latest revision as of 14:01, 2 January 2020

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DLMF:22.8.E1
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    Statements

    test
    sn ⁡ ( u + v ) = sn ⁡ u ⁢ cn ⁡ v ⁢ dn ⁡ v + sn ⁡ v ⁢ cn ⁡ u ⁢ dn ⁡ u 1 - k 2 ⁢ sn 2 ⁡ u ⁢ sn 2 ⁡ v , Jacobi-elliptic-sn 𝑢 𝑣 𝑘 Jacobi-elliptic-sn 𝑢 𝑘 Jacobi-elliptic-cn 𝑣 𝑘 Jacobi-elliptic-dn 𝑣 𝑘 Jacobi-elliptic-sn 𝑣 𝑘 Jacobi-elliptic-cn 𝑢 𝑘 Jacobi-elliptic-dn 𝑢 𝑘 1 superscript 𝑘 2 Jacobi-elliptic-sn 2 𝑢 𝑘 Jacobi-elliptic-sn 2 𝑣 𝑘 {\displaystyle{\displaystyle\operatorname{sn}(u+v)=\frac{\operatorname{sn}u% \operatorname{cn}v\operatorname{dn}v+\operatorname{sn}v\operatorname{cn}u% \operatorname{dn}u}{1-k^{2}{\operatorname{sn}^{2}}u{\operatorname{sn}^{2}}v},}}
    0 references
    DLMF id
    DLMF:22.8.E1
    0 references
    Symbols used
    Jacobian elliptic function
    test
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2adec
    0 references
    Jacobian elliptic function
    test
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2adec
    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.m2adec
    0 references
    Q11991
    test
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C22.S8.XMD1.m1dec
    0 references
    Q11992
    test
    v 𝑣 {\displaystyle{\displaystyle v}}
    xml-id
    C22.S8.XMD2.m1dec
    0 references
    Q11993
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S8.XMD3.m1dec
    0 references
     
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