Formula:7661

Digital Library of Mathematical Functions ID 22.8.E3

${\displaystyle{\displaystyle\operatorname{dn}(u+v)=\frac{\operatorname{dn}u\operatorname{dn}v-k^{2}\operatorname{sn}u\operatorname{cn}u\operatorname{sn}v\operatorname{cn}v}{1-k^{2}{\operatorname{sn}^{2}}u{\operatorname{sn}^{2}}v}.}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle u}}$: complex
• ${\displaystyle{\displaystyle v}}$: complex
• ${\displaystyle{\displaystyle k}}$: modulus
 

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