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Line 181: ==Definition in terms of the Jacobi theta functions== ===Using elliptic integrals=== Equivalently, Jacobi's elliptic functions can be defined in terms of the [[theta function]]s.<ref>{{cite book \|last1=Whittaker \|first1=Edmund Taylor \|authorlink1=Edmund T. Whittaker \|last2=Watson \|first2=George Neville \|authorlink2=George N. Watson \|date= 1927 \|page=492 \|edition=4th \|title=A Course of Modern Analysis \|title-link=A Course of Modern Analysis \|publisher= Cambridge University Press}}</ref> ~~Let~~With <math>z,\tau\in\mathbb{C}</math> such that <math>\operatorname{Im}\tau >0</math>, let :<math>\theta_1(z\|\tau)=\displaystyle\sum_{n=-\infty}^\infty (-1)^{n-\frac12}e^{(2n+1)iz+\pi i\tau\left(n+\frac12\right)^2},</math>

Jacobi elliptic functions: Difference between revisions