DLMF:22.7.E3 (Q6959)

From DRMF
Revision as of 15:00, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:22.7.E3
No description defined

    Statements

    Defining formula
    cn ⁡ ( z , k ) = cn ⁡ ( z / ( 1 + k 1 ) , k 1 ) ⁢ dn ⁡ ( z / ( 1 + k 1 ) , k 1 ) 1 + k 1 ⁢ sn 2 ⁡ ( z / ( 1 + k 1 ) , k 1 ) , Jacobi-elliptic-cn 𝑧 𝑘 Jacobi-elliptic-cn 𝑧 1 subscript 𝑘 1 subscript 𝑘 1 Jacobi-elliptic-dn 𝑧 1 subscript 𝑘 1 subscript 𝑘 1 1 subscript 𝑘 1 Jacobi-elliptic-sn 2 𝑧 1 subscript 𝑘 1 subscript 𝑘 1 {\displaystyle{\displaystyle\operatorname{cn}\left(z,k\right)=\frac{% \operatorname{cn}\left(z/(1+k_{1}),k_{1}\right)\operatorname{dn}\left(z/(1+k_{% 1}),k_{1}\right)}{1+k_{1}{\operatorname{sn}^{2}}\left(z/(1+k_{1}),k_{1}\right)% },}}
    0 references
    DLMF id
    DLMF:22.7.E3
    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.m2adec
    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.m2adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6959&oldid=53270"