Thanks, Rich! Perhaps I should generalize my question: are there any interesting uses of _ellipses_ (not just circles) in the _complex_ plane ? At 01:28 PM 2/12/2013, rcs@xmission.com wrote:
No. Elliptic functions have two periods, with a non-real ratio. The periods define a "period parallelogram". The input is usally scaled so that one period is real, typically either 1 or 2pi. Interesting special cases arise when one period is 1 and the other is i or w = 1/2 + i sqrt3 /2. If I remember correctly, each pargrm must have either two poles or a double pole (at least) and a matching number of zeros. Salamin's the expert at this. Abramowitz & Stegun is an OK beginning introduction. I don't know about DLMF.
Rich
--- Quoting Henry Baker <hbaker1@pipeline.com>:
Are elliptical regions (those conic sections with 2 foci) in the complex plane particularly interesting in the study of "elliptic functions" ??
I don't know enough about elliptic functions to have any insights here.