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<div class="moz-cite-prefix">Hi Lester</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Please be reminded of the correct
spelling : Riemann</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Cheers,</div>
<div class="moz-cite-prefix">Claus</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">On 29-11-2021 18:23, Lester Anderson
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAE3taFAp4afB=RU710mR=Aaks5x-U=sh1ehsj-8f1Ldrfkpg2Q@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<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">
</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"
moz-do-not-send="true" class="moz-txt-link-freetext">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"
moz-do-not-send="true" class="moz-txt-link-freetext">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>
> users mailing list<br>
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moz-do-not-send="true" class="moz-txt-link-freetext">users@lists.scilab.org</a><br>
> <a href="http://lists.scilab.org/mailman/listinfo/users"
rel="noreferrer" target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">http://lists.scilab.org/mailman/listinfo/users</a><br>
<br>
</blockquote>
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<br>
<fieldset class="moz-mime-attachment-header"></fieldset>
<pre class="moz-quote-pre" wrap="">_______________________________________________
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