<div dir="ltr">Hi all,<div><br></div><div>Found a bit of Matlab/Octave code to solve the Reimann Zeta function for values >= 0, not perfect but it's a start. Need to figure out how to deal with negative values.</div><div><br></div><div>Lester</div><div><br></div><div><pre style="font-family:Monospaced"><span style="color:rgb(100,174,100);font-style:italic">// Reimann Zeta function: valid for t </span><span style="color:rgb(100,174,100);font-style:italic">></span><span style="color:rgb(100,174,100);font-style:italic">= 0</span>
<span style="color:rgb(176,24,19)">function</span> <span style="color:rgb(131,67,16);font-weight:bold">f</span><span style="color:rgb(92,92,92)">=</span><span style="color:rgb(0,0,0);text-decoration-line:underline">F</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(131,67,16);font-weight:bold">x</span><span style="color:rgb(74,85,219)">)</span>
<span style="color:rgb(131,67,16);font-weight:bold">f</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(188,143,143)">1.</span><span style="color:rgb(92,92,92)">/</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(50,185,185)">gamma</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">.*</span><span style="color:rgb(131,67,16);font-weight:bold">x</span><span style="color:rgb(92,92,92)">.^</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">./</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(50,185,185)">exp</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(131,67,16);font-weight:bold">x</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(176,24,19)">endfunction</span>
<span style="color:rgb(176,24,19)">function</span> <span style="color:rgb(74,85,219)">[</span><span style="color:rgb(131,67,16);font-weight:bold">z</span><span style="color:rgb(74,85,219)">]</span><span style="color:rgb(92,92,92)">=</span><span style="color:rgb(0,0,0);text-decoration-line:underline">zeta</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">)</span>
<span style="color:rgb(50,185,185)">global</span> <span style="color:rgb(188,143,143)">x</span>
<span style="color:rgb(131,67,16);font-weight:bold">z</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(50,185,185)">zeros</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(50,185,185)">size</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(160,32,240)">for</span> <span style="color:rgb(0,0,0)">j</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(188,143,143)">1</span><span style="color:rgb(255,170,0)">:</span><span style="color:rgb(50,185,185)">prod</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(50,185,185)">size</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span>
<span style="color:rgb(160,32,240)">if</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(50,185,185)">real</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">>=</span> <span style="color:rgb(188,143,143)">0</span><span style="color:rgb(74,85,219)">)</span>
<span style="color:rgb(160,32,240)">if</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(50,185,185)">imag</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">==</span> <span style="color:rgb(188,143,143)">0</span> <span style="color:rgb(92,92,92)">&</span><span style="color:rgb(92,92,92)">&</span> <span style="color:rgb(50,185,185)">real</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">></span> <span style="color:rgb(188,143,143)">1</span><span style="color:rgb(74,85,219)">)</span>
<span style="color:rgb(131,67,16);font-weight:bold">z</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(50,185,185)">intg</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(188,143,143)">0</span><span style="color:rgb(0,0,0)">,</span><span style="color:rgb(188,143,143)">200</span><span style="color:rgb(0,0,0)">,</span><span style="color:rgb(0,0,0);text-decoration-line:underline">F</span><span style="color:rgb(74,85,219)">)</span>
<span style="color:rgb(160,32,240)">elseif</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">==</span> <span style="color:rgb(188,143,143)">0</span><span style="color:rgb(74,85,219)">)</span>
<span style="color:rgb(131,67,16);font-weight:bold">z</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">0.5</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(160,32,240)">elseif</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">==</span> <span style="color:rgb(188,143,143)">1</span><span style="color:rgb(74,85,219)">)</span>
<span style="color:rgb(131,67,16);font-weight:bold">z</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(218,112,214)">%inf</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(160,32,240)">else</span>
<span style="color:rgb(160,32,240)">for</span> <span style="color:rgb(0,0,0)">k</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(188,143,143)">1</span><span style="color:rgb(255,170,0)">:</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(255,170,0)">:</span><span style="color:rgb(188,143,143)">100</span>
<span style="color:rgb(131,67,16);font-weight:bold">z</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(74,85,219)">(</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">.^</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">k</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">./</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">k</span><span style="color:rgb(92,92,92)">.^</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(160,32,240)">end</span>
<span style="color:rgb(131,67,16);font-weight:bold">z</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(188,143,143)">1.</span><span style="color:rgb(92,92,92)">/</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">2.</span><span style="color:rgb(92,92,92)">^</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">.*</span><span style="color:rgb(131,67,16);font-weight:bold">z</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(160,32,240)">end</span>
<span style="color:rgb(160,32,240)">else</span>
<span style="color:rgb(131,67,16);font-weight:bold">z</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span> <span style="color:rgb(92,92,92)">=</span> <span style="color:rgb(188,143,143)">2.</span><span style="color:rgb(92,92,92)">^</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">.*</span><span style="color:rgb(218,112,214)">%pi</span><span style="color:rgb(92,92,92)">.^</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">.*</span><span style="color:rgb(50,185,185)">sin</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(218,112,214)">%pi</span><span style="color:rgb(92,92,92)">.*</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">./</span><span style="color:rgb(188,143,143)">2</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">.*</span><span style="color:rgb(50,185,185)">gamma</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(92,92,92)">.*</span><span style="color:rgb(0,0,0);text-decoration-line:underline">zeta</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(188,143,143)">1</span><span style="color:rgb(92,92,92)">-</span><span style="color:rgb(131,67,16);font-weight:bold">t</span><span style="color:rgb(74,85,219)">(</span><span style="color:rgb(0,0,0)">j</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(74,85,219)">)</span><span style="color:rgb(0,0,0)">;</span>
<span style="color:rgb(160,32,240)">end</span>
<span style="color:rgb(160,32,240)">end</span>
<span style="color:rgb(176,24,19)">endfunction</span></pre><pre style="font-family:Monospaced"><br></pre></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, 29 Nov 2021 at 08:51, Heinz Nabielek <<a href="mailto:heinznabielek@me.com">heinznabielek@me.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Riemann zeta function !<br>
<br>
Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.<br>
<br>
Heinz<br>
<br>
<br>
<br>
> On 29.11.2021, at 09:39, Lester Anderson <<a href="mailto:arctica1963@gmail.com" target="_blank">arctica1963@gmail.com</a>> wrote:<br>
> <br>
> Hello all,<br>
> <br>
> I am interested in the Reimann Zeta function, but it does not appear as an option directly with Scilab (v6.1.1).<br>
> <br>
> Has anyone already prepared a function for this?<br>
> <br>
> Lester<br>
> _______________________________________________<br>
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> <a href="http://lists.scilab.org/mailman/listinfo/users" rel="noreferrer" target="_blank">http://lists.scilab.org/mailman/listinfo/users</a><br>
<br>
</blockquote></div>