Formula:7710

Digital Library of Mathematical Functions ID 22.10.E2

${\displaystyle{\displaystyle\operatorname{cn}\left(z,k\right)=1-\frac{z^{2}}{2!}+\left(1+4k^{2}\right)\frac{z^{4}}{4!}-\left(1+44k^{2}+16k^{4}\right)\frac{z^{6}}{6!}+O\left(z^{8}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle z}}$: complex
• ${\displaystyle{\displaystyle k}}$: modulus
 

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