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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="DedekindEta"></a>
DedekindEta
</h2>

Calculates the value of Dedekind's \eta-function.

<p><p>

<h3>
Syntax:
</h3>
<pre>u := DedekindEta(z);</pre>

<p>

<table>
<tr>
<td>complex</td>
<td><pre>  u  </pre></td>
<td></td>
</tr>
<tr>
<td>complex</td>
<td><pre>  z  </pre></td>
<td>complex number with Im(z)>0</td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Let z be a complex number with Im(z)>0. The value
 \eta(z)=q^{1/24}\prod_{n=1}^{\infty}(1-q^n)

of the Dedekind's \eta-function (with q=e^{2cdot\picdot icdot z})
is
then a well-defined complex number. It is determined by
writing the infinite product as a (quickly converging)
infinite sum and calculating this sum up to a certain
precision, that depends on the precision of the defining
complex field. For further information about the algorithm see
Scherz.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute \eta(1+\sqrt{-5}):
<pre>

kash> DedekindEta(1+Sqrt(-5));
> 0.5379066478127104520437266840371093596748318066880552 + 0.1441316518847481027\
896657792883659909845154545709301*i

</pre>

<p>


<hr>

<p>
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