How to realize Riemann Siegel Theta Function with MATLAB?
However in MATLAB, the gamma function seems to be defined only for a real variable, unless you use the symbolic toolbox version of gamma. So this should work:
t = (1:5)'; [t,angle(double(gamma(sym(1/4 + i*t/2)))) - log(pi)/2*t] ans = 1 -1.76754795281229 2 -2.52591091881613 3 -2.99456469601083 4 -3.29063503121648 5 -3.45962037536346
That is valid for real arguments t. I'd need to do some reading to know if this works for complex arguments, though I assume it does not, since I gave indicates it is valid for real arguments. Hopefully you care only about real arguments, and are uninterested in an extension to the complex plane.
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