
<A NAME=ZETA>

<TITLE>ZETA</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>ZETA</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
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The <em>Zeta</em> operator returns Riemann's Zeta function, 
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Zeta (z) := sum(1/(k**z),k,1,infinity) 
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syntax: </H3>
<em>Zeta</em>(&lt;expression&gt;) 
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examples: </H3>
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Zeta(2); 

    2
  pi  / 6 


on rounded; 

Zeta 1.01; 

  100.577943338

</TT></PRE><P>Numerical computation for the Zeta function for arguments close to
 1 are 
tedious, because the series is converging very slowly. In this case a formula 
(e.g. found in Bender/Orzag: Advanced Mathematical Methods for 
Scientists and Engineers, McGraw-Hill) is used. 
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No numerical approximation for complex arguments is done. 
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