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English: Plots of the phase for the twelve Jacobi Elliptic functions pq(u,m) as a function complex argument u, with poles and zeroes indicated. The plots are over one full cycle in the real and imaginary directions with the colored portion indicating phase according to the color wheel at the lower right (which replaces the trivial dd function). Regions with amplitude below 1/3 are colored black, roughly indicating the location of a zero, while regions with amplitude above 3 are colored white, roughly indicating the position of a pole. All plots use m=2/3 with K=K(m), K'=K(1-m), K(.) being the complete elliptic integral of the first kind. Arrows at the poles point in direction of zero phase. Right and left arrows imply positive and negative real residues respectively. Up and down arrows imply positive and negative imaginary residues respectively.
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Author PAR
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This diagram was created with Mathematica by PAR.

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10 January 2018

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Date/TimeThumbnailDimensionsUserComment
current12:19, 25 January 2018Thumbnail for version as of 12:19, 25 January 20181,250 × 1,250 (338 KB)PARLable axes in K and K' to conform to notation in the Jacobi elliptic functions article. Add arrows on poles pointing in the zero phase direction.
20:59, 10 January 2018Thumbnail for version as of 20:59, 10 January 20181,250 × 1,250 (335 KB)PARUser created page with UploadWizard

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