Formula:7644

Digital Library of Mathematical Functions ID 22.6.E17

${\displaystyle{\displaystyle\frac{1-\operatorname{cn}\left(2z,k\right)}{1+\operatorname{cn}\left(2z,k\right)}=\frac{{\operatorname{sn}^{2}}\left(z,k\right){\operatorname{dn}^{2}}\left(z,k\right)}{{\operatorname{cn}^{2}}\left(z,k\right)},}}$

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
• ${\displaystyle{\displaystyle z}}$: complex
• ${\displaystyle{\displaystyle k}}$: modulus
 

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