You can do abs(gamma(z)) as a contour plot, and you and do exp(i arg(gamma(z))) in color and not have to worry about the discontinuity in arg(gamma(z)). You can even do a color contour plot showing both together. But arg(gamma(z)) is multiple valued and depends on which way you go around the poles. It may be of some use to note that 1/gamma(z) is an entire function. -- Gene
________________________________ From: Fred Lunnon <fred.lunnon@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Saturday, March 29, 2014 5:19 PM Subject: [math-fun] Continuous argument
Preparing a seminar on binomial coefficient extension --- avoiding the nuclear option? --- for a computer science audience, I prepared plots of re, im, abs, arg parts of the gamma function qua function of a complex variable. It struck me that the arg plot would be much improved if one could avoid it snapping back to the principal value when passing thru' angles (+/1)pi --- proceeding instead continuously in whichever direction happened to be current at that point.
How can arg() be hacked to achieve such an effect?
[ Note that arg(gamma(z)) really is discontinuous around the poles at non-positive integer z --- but that is not an issue here, since special measures must be taken in that neighbourhood anyway. Rather appropriate subject line for the list, what? ]
Fred Lunnon
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