Formula:7716

Digital Library of Mathematical Functions ID 22.10.E8

${\displaystyle{\displaystyle\operatorname{cn}\left(z,k\right)=\operatorname{sech}z+\frac{{k^{\prime}}^{2}}{4}(z-\sinh z\cosh z)\tanh z\operatorname{sech}z+O\left({k^{\prime}}^{4}\right),}}$

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
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}$: hyperbolic secant function
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\tanh\NVar{z}}}$: hyperbolic tangent function
• ${\displaystyle{\displaystyle z}}$: complex
• ${\displaystyle{\displaystyle k}}$: modulus
• ${\displaystyle{\displaystyle k^{\prime}}}$: complementary modulus
 

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