DLMF:22.8.E3 (Q6968)

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DLMF:22.8.E3
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    Statements

    Defining formula
    dn ⁡ ( u + v ) = dn ⁡ u ⁢ dn ⁡ v - k 2 ⁢ sn ⁡ u ⁢ cn ⁡ u ⁢ sn ⁡ v ⁢ cn ⁡ v 1 - k 2 ⁢ sn 2 ⁡ u ⁢ sn 2 ⁡ v . Jacobi-elliptic-dn 𝑢 𝑣 𝑘 Jacobi-elliptic-dn 𝑢 𝑘 Jacobi-elliptic-dn 𝑣 𝑘 superscript 𝑘 2 Jacobi-elliptic-sn 𝑢 𝑘 Jacobi-elliptic-cn 𝑢 𝑘 Jacobi-elliptic-sn 𝑣 𝑘 Jacobi-elliptic-cn 𝑣 𝑘 1 superscript 𝑘 2 Jacobi-elliptic-sn 2 𝑢 𝑘 Jacobi-elliptic-sn 2 𝑣 𝑘 {\displaystyle{\displaystyle\operatorname{dn}(u+v)=\frac{\operatorname{dn}u% \operatorname{dn}v-k^{2}\operatorname{sn}u\operatorname{cn}u\operatorname{sn}v% \operatorname{cn}v}{1-k^{2}{\operatorname{sn}^{2}}u{\operatorname{sn}^{2}}v}.}}
    0 references
    DLMF id
    DLMF:22.8.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.m2abdec
    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.m2abdec
    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.m2abdec
    0 references
    Q11991
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C22.S8.XMD1.m1bdec
    0 references
     
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