Formula:7663

Digital Library of Mathematical Functions ID 22.8.E5

${\displaystyle{\displaystyle\operatorname{sd}(u+v)=\frac{\operatorname{sd}u\operatorname{cd}v\operatorname{nd}v+\operatorname{sd}v\operatorname{cd}u\operatorname{nd}u}{1+k^{2}{k^{\prime}}^{2}{\operatorname{sd}^{2}}u{\operatorname{sd}^{2}}v},}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\operatorname{nd}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle u}}$: complex
• ${\displaystyle{\displaystyle v}}$: complex
• ${\displaystyle{\displaystyle k}}$: modulus
 

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