DLMF:22.8.E18 (Q6983)

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DLMF:22.8.E18
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    Statements

    Defining formula
    dn ⁡ ( u + v ) = cn ⁡ u ⁢ dn ⁡ u ⁢ cn ⁡ v ⁢ dn ⁡ v + k ′ 2 ⁢ sn ⁡ u ⁢ sn ⁡ v cn ⁡ u ⁢ cn ⁡ v + sn ⁡ u ⁢ dn ⁡ u ⁢ sn ⁡ v ⁢ dn ⁡ v . Jacobi-elliptic-dn 𝑢 𝑣 𝑘 Jacobi-elliptic-cn 𝑢 𝑘 Jacobi-elliptic-dn 𝑢 𝑘 Jacobi-elliptic-cn 𝑣 𝑘 Jacobi-elliptic-dn 𝑣 𝑘 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sn 𝑢 𝑘 Jacobi-elliptic-sn 𝑣 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{dn}(u+v)=\frac{\operatorname{cn}u% \operatorname{dn}u\operatorname{cn}v\operatorname{dn}v+{k^{\prime}}^{2}% \operatorname{sn}u\operatorname{sn}v}{\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.E18
    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.m2ahdec
    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.m2ahdec
    0 references
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2ahdec
    0 references
    Q11994
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C22.S8.XMD4.m1edec
    0 references
    Q11995
    Defining formula
    v 𝑣 {\displaystyle{\displaystyle v}}
    xml-id
    C22.S8.XMD5.m1edec
    0 references
    Q11996
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S8.XMD6.m1edec
    0 references
     
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