cln_mirror/doc/ratseries/slides/slide5.tex

\input amssym.def
\input amssym
\magnification=\magstep3
\hsize=17truecm
\vsize=19truecm
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\parindent=0mm
\font\eins=cmb10 scaled \magstep 3
\font\zwei=cmr12
\font\mini=cmr7
\def\frac#1#2{{{#1} \over {#2}}}
\hbox{}
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\centerline{\eins Other Applications}
\bigskip\bigskip
\item{$\bullet$} exp, sin, cos, log, arctan, etc.
\medskip
\item{$\bullet$} $\pi$ (Chudnovsky's formula, a Ramanujan type series)
\medskip
\item{$\bullet$} hypergeometric functions at $x \in {\Bbb Q}$
\medskip
\item{$\bullet$} hypergeometric and holonomic functions at $x \in {\Bbb C}$
     [J.\ van der Hoeven]
\medskip
\item{$\bullet$} $\Gamma(x)$ at $x \in {\Bbb Q}$
\medskip
\item{$\bullet$} Large terms of P-recursive sequences, i.e.\ $f_n$ ($n$ large)
     where ${f(x) = \sum f_n x^n}$ is holonomic,
\medskip
\item{$\bullet$} $\zeta(k)$, $k > 1$ odd (using Cohen-Villegas-Zagier
     convergence acceleration)

\vfill
\hbox{}
\eject

\end