<html>
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
  </head>
  <body>
    <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>
          > <a href="mailto:users@lists.scilab.org" target="_blank"
            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>
      </div>
      <br>
      <fieldset class="moz-mime-attachment-header"></fieldset>
      <pre class="moz-quote-pre" wrap="">_______________________________________________
users mailing list
<a class="moz-txt-link-abbreviated" href="mailto:users@lists.scilab.org">users@lists.scilab.org</a>
<a class="moz-txt-link-freetext" href="http://lists.scilab.org/mailman/listinfo/users">http://lists.scilab.org/mailman/listinfo/users</a>
</pre>
    </blockquote>
    <p><br>
    </p>
  </body>
</html>