DLMF:22.8.E14 (Q6979): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
Defining formula:

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.m2addec

Revision as of 15:04, 2 January 2020

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DLMF:22.8.E14
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    Statements

    Defining formula
    sn ⁡ ( u + v ) = sn ⁡ u ⁢ cn ⁡ u ⁢ dn ⁡ v + sn ⁡ v ⁢ cn ⁡ v ⁢ dn ⁡ u cn ⁡ u ⁢ cn ⁡ v + sn ⁡ u ⁢ dn ⁡ u ⁢ sn ⁡ v ⁢ dn ⁡ v , Jacobi-elliptic-sn 𝑢 𝑣 𝑘 Jacobi-elliptic-sn 𝑢 𝑘 Jacobi-elliptic-cn 𝑢 𝑘 Jacobi-elliptic-dn 𝑣 𝑘 Jacobi-elliptic-sn 𝑣 𝑘 Jacobi-elliptic-cn 𝑣 𝑘 Jacobi-elliptic-dn 𝑢 𝑘 Jacobi-elliptic-cn 𝑢 𝑘 Jacobi-elliptic-cn 𝑣 𝑘 Jacobi-elliptic-sn 𝑢 𝑘 Jacobi-elliptic-dn 𝑢 𝑘 Jacobi-elliptic-sn 𝑣 𝑘 Jacobi-elliptic-dn 𝑣 𝑘 {\displaystyle{\displaystyle\operatorname{sn}(u+v)=\frac{\operatorname{sn}u% \operatorname{cn}u\operatorname{dn}v+\operatorname{sn}v\operatorname{cn}v% \operatorname{dn}u}{\operatorname{cn}u\operatorname{cn}v+\operatorname{sn}u% \operatorname{dn}u\operatorname{sn}v\operatorname{dn}v},}}
    0 references
    DLMF id
    DLMF:22.8.E14
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2addec
    0 references
    Jacobian elliptic function
    Defining formula
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2addec
    0 references
     
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