Addition formula for Jacobi elliptic function sn

 

\mbox{sn}(u+v) = \frac{\mbox{sn}\, u\, \mbox{cn} \,v\, \mbox{dn} \,v\, + \mbox{sn}\,v\, \mbox{cn} \,u\, \mbox{dn} \, u}{ 1 - k^2 \, \mbox{sn}^2\, u\, \mbox{sn}^2 \,v}