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%%a Plain TeX file by Shalosh B. Ekhad and Doron Zeilberger (x pages)

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\centerline
{\bf Computing Pi as Slowly as Possible }
\bigskip
\centerline
{\it Shalosh B. EKHAD and Doron ZEILBERGER}

$$
\frac {{{2n} \choose {n}}}{4^n}=
\frac{1}{\sqrt{n}} \frac{1}{\sqrt{\pi}} \cdot
$$
$$
(
1-1/8\,{n}^{-1}+{\frac {1}{128}}\,{n}^{-2}+{\frac {5}{1024}}\,{n}^{-3}-{\frac {21}{32768}}\,{n}^{-4}-{\frac {399}{262144}}\,{n}^{-5}
$$
$$
+{\frac {869}{4194304}}
\,{n}^{-6}+{\frac {39325}{33554432}}\,{n}^{-7}-{\frac {334477}{2147483648}}\,{n}^{-8}-{\frac {28717403}{17179869184}}\,{n}^{-9}+{\frac {59697183}{
274877906944}}\,{n}^{-10}
$$
$$
+{\frac {8400372435}{2199023255552}}\,{n}^{-11}-{\frac {34429291905}{70368744177664}}\,{n}^{-12}-{\frac {7199255611995}{
562949953421312}}\,{n}^{-13}
$$
$$
+{\frac {14631594576045}{9007199254740992}}\,{n}^{-14}+{\frac {4251206967062925}{72057594037927936}}\,{n}^{-15}-{\frac {
68787420596367165}{9223372036854775808}}\,{n}^{-16}
$$
$$
-{\frac {26475975382085110035}{73786976294838206464}}\,{n}^{-17}+{\frac {53392138323683746235}{
1180591620717411303424}}\,{n}^{-18}
$$
$$
+{\frac {26275374869163335461975}{9444732965739290427392}}\,{n}^{-19}-{\frac {105772979046693606062363}{302231454903657293676544}}\,{n}^{-20}
+O(n^{-21}) )
$$

\bigskip
{\bf References}

\bigskip
\hrule
\bigskip
Shalosh B. Ekhad, c/o D. Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen
Rd., Piscataway, NJ 08854-8019, USA. \hfill\break
Email: {\tt ShaloshBEkhad at gmail dot com}   \quad .
\bigskip
Doron Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen
Rd., Piscataway, NJ 08854-8019, USA. \hfill\break
Email: {\tt DoronZeil at gmail  dot com}   \quad .


\end





