Lemniscate elliptic functions: Difference between revisions

Revision as of 07:17, 24 June 2008

Revision as of 20:30, 6 November 2009

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In the lemniscatic case, the minimal half period <math>\omega_1</math> is real and equal to

:<math>\frac{\Gamma^2(\fractfrac{1}{4})}{4\sqrt{\pi}}</math>

where <math>\Gamma</math> is the [[Gamma function]]. The second smallest half period is pure imaginary

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:<math>

e_1=\fractfrac{1}{2},\qquad

e_2=0,\qquad

e_3=-\fractfrac{1}{2}.

</math>