Formula:7633

Digital Library of Mathematical Functions ID 22.6.E6

${\displaystyle{\displaystyle\operatorname{cn}\left(2z,k\right)=\frac{{\operatorname{cn}^{2}}\left(z,k\right)-{\operatorname{sn}^{2}}\left(z,k\right){\operatorname{dn}^{2}}\left(z,k\right)}{1-k^{2}{\operatorname{sn}^{4}}\left(z,k\right)}=\frac{{\operatorname{cn}^{4}}\left(z,k\right)-{k^{\prime}}^{2}{\operatorname{sn}^{4}}\left(z,k\right)}{1-k^{2}{\operatorname{sn}^{4}}\left(z,k\right)},}}$

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
• ${\displaystyle{\displaystyle k^{\prime}}}$: complementary modulus
 

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