Jacobi elliptic functions: Difference between revisions

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==Approximation in terms of hyperbolic functions==

The Jacobi elliptic functions can be expanded in terms of the hyperbolic functions. When <math>m</math> is close to unity, such that <math>m'^2</math> and higher powerpowers of <math>m'</math> can be neglected, we have:

* sn(''u''):

::<math>\operatorname{sn} (u,m)\approx \tanh (u)+\frac{1}{4}m'(\sinh (u)\cosh (u) -u)\operatorname{sech}^2 (u).</math>