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Equianharmonic
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In mathematics, and in particular the study of Weierstrass elliptic functions, the equianharmonic case occurs when the Weierstrass invariants satisfy g2 = 0 and g3 = 1.[1] This page follows the terminology of Abramowitz and Stegun; see also the lemniscatic case. (These are special examples of complex multiplication.)
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In the equianharmonic case, the minimal half period ω2 is real and equal to
where is the Gamma function. The half period is
Here the period lattice is a real multiple of the Eisenstein integers.
The constants e1, e2 and e3 are given by
The case g2 = 0, g3 = a may be handled by a scaling transformation.
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