Formula:7631

Digital Library of Mathematical Functions ID 22.6.E4

${\displaystyle{\displaystyle-k^{2}{k^{\prime}}^{2}{\operatorname{sd}^{2}}\left(z,k\right)=k^{2}({\operatorname{cd}^{2}}\left(z,k\right)-1)={k^{\prime}}^{2}(1-{\operatorname{nd}^{2}}\left(z,k\right)).}}$

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

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