# Xi function plotter ??

i would like to know what software i need to plot the RIemann Xi function

$\xi(s)= \frac{1}{2}s(s-1)\Gamma (s/2)\zeta (s)$ on a given interval , for example

from $s=0 , s=1000$ or from $s=0 , s=10^{6}$ and similar.. thanks in advance.

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Just a browser: Wolfram – draks ... Jul 4 '12 at 11:33
$\Gamma(\cdot)$ can get pretty big, which will make one tail of the graph dwarf everything. Do you perhaps want $\mathrm{Im}(s)$ in the given bounds with $\mathrm{Re}(s)$ in $(0,1)$? – anon Jul 4 '12 at 11:36
am not i was interested in the $\xi (s)$ function to compare a method to obtain the Riemann Zeros and Riemann zeta function as a functional determinant with the known values of Riemann Xi function.. thanks anyway – Jose Garcia Jul 4 '12 at 11:38
Seriously, it looks like a vertical line (that's just up to $s=10^3$; good luck with $10^6\,$!); I do not see what purpose the graph by itself could serve. Perhaps if you wanted to compare $\xi$ to some (practically computable) functional determinant candidates in various ways, some graphical methods could help. (And even then I wonder why you're interested in the real line rather than the critical strip.) – anon Jul 4 '12 at 11:46
the idea is to see if the Riemann Xi function is a functional determinant in the sense $det(H+(s-1)s)$ of a certain Hamiltonian oeprator with potential defined by $f^{-1}(x)= 2 \sqrt \pi \frac{d^{1/2}}{dx^{1/2}} \frac{1}{\pi}arg\xi(1/2+i \sqrt x)$ – Jose Garcia Jul 4 '12 at 13:03