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.