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I am writing a simple program to generate the zero's of the Riemann zeta function accurately.

However I need the first say, ten terms of the theta function

[tex]\theta\left(x\right) = arg\left(\Gamma\left(\frac{2ix+1}{4}\right)\right)-\frac{xln\pi}{2}[/tex]

to get an acceptably accurate answer.

Wikipedia gives an approximation here;

http://en.wikipedia.org/wiki/Riemann%E2%80%93Siegel_theta_function" [Broken]

but I need a larger expansion of the series

I tried to get MATLAB to generate the terms but am having no luck,

The algorithm is basically using Siegels Z-function and detecting a change of sign.

However, as the language I am using (a very basic pseudocode) is incapable of calculating the gamma function, I need the theta function to be expanded in the way it has been on the wiki page but with more terms so the algorithm can calculate the value approximately.

Sorry if this doesn't really make sense, but I am hoping someone here can help.

Thankyou

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# Riemann-Siegel Theta Function Approximation

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