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\magnification=\magstep3\hsize=19truecm\vsize=19truecm\nopagenumbers\parindent=0mm\font\eins=cmb10 scaled \magstep 3\font\zwei=cmr12\font\mini=cmr7\def\frac#1#2{{{#1} \over {#2}}}\hbox{}\vfill
\centerline{\eins Main Result}\bigskip\bigskip\centerline{$\displaystyle S = {\sum\limits_{n=0}^{\infty} \frac{a(n)}{b(n)} \, \frac{p(0) \cdots p(n)}{q(0) \cdots q(n)}}$}\bigskipwith $a(n)$, $b(n)$, $p(n)$, $q(n)$ small integers ${} = O(n^c)$\bigskipcan be computed to $N$ digits in time\medskip\centerline{$O \left( {M(N) \, {(\log N)}^2} \right)
= O \left( N \, {(\log N)}^3 \, \log \log N \right)$.}
\vfill\hbox{}\eject
\end
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