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Equianharmonic : ウィキペディア英語版
Equianharmonic

In mathematics, and in particular the study of Weierstrass elliptic functions, the equianharmonic case occurs when the Weierstrass invariants satisfy ''g''2 = 0 and ''g''3 = 1.
This page follows the terminology of Abramowitz and Stegun; see also the lemniscatic case. (These are special examples of complex multiplication.)
In the equianharmonic case, the minimal half period ω2 is real and equal to
:\frac
where \Gamma is the Gamma function. The half period is
:\omega_1=\tfrac(-1+\sqrt3i)\omega_2.
Here the period lattice is a real multiple of the Eisenstein integers.
The constants ''e''1, ''e''2 and ''e''3 are given by
:
e_1=4^e^,\qquad
e_2=4^,\qquad
e_3=4^e^.

The case ''g''2 = 0, ''g''3 = ''a'' may be handled by a scaling transformation.


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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