30A99-TopicEntryOnSeries.tex

\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{TopicEntryOnSeries}
\pmcreated{2013-03-22 17:27:59}
\pmmodified{2013-03-22 17:27:59}
\pmowner{pahio}{2872}
\pmmodifier{pahio}{2872}
\pmtitle{topic entry on series}
\pmrecord{25}{39851}
\pmprivacy{1}
\pmauthor{pahio}{2872}
\pmtype{Topic}
\pmcomment{trigger rebuild}
\pmclassification{msc}{30A99}
\pmsynonym{topic entry on series of complex terms}{TopicEntryOnSeries}

\endmetadata

% this is the default PlanetMath preamble.  as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.

% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{multicol}

% used for TeXing text within eps files
%\usepackage{psfrag}
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%\usepackage{graphicx}
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\theoremstyle{definition}
\newtheorem*{thmplain}{Theorem}

\begin{document}
\PMlinkescapeword{term} \PMlinkescapeword{terms}

There are in PM many entries on series whose terms are usually thought to be real but which can equally well be any complex numbers.  It may be good to make a list of such entries, but of course include such ones concerning the proper complex (imaginary) term series.

\begin{multicols}{2}
\begin{enumerate}
\item \PMlinkname{series}{Series}
\item convergent series
\item determining series convergence
\item convergence of complex term series
\item sum of series
\item remainder term
\item finite changes in convergent series
\item manipulating convergent series
\item Riemann's theorem on rearrangements
\item necessary condition of convergence
\item harmonic series
\item \PMlinkid{convergent series where not only $a_n$ but also $na_n$ tends to 0}{11941}
\item \PMlinkname{generalization of Olivier criterion}{AGeneralisationOfOlivierCriterion}
\item slower convergent series
\item slower divergent series
\item adding and removing parentheses in series
\item absolute convergence theorem
\item limit of sequence as sum of series
\item sum of series depends on order
\item conditionally convergent real series
\item multiplication of series
\item Cauchy product
\item double series
\item absolute convergence of double series
\item Dirichlet series
\item convergence of Riemann zeta series
\item example of summation by parts
\item real part series and imaginary part series
\item sum function of series
\item termwise differentiation
\item theorems on complex function series
\item power series
\item identity theorem of power series
\item Taylor series
\item Laurent series
\item binomial theorem
\item quotient of Taylor series
\item Abel summability
\item Weierstrass double series theorem
\item infinity sum of reciprocal numbers
\end{enumerate}
\end{multicols}

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\end{document}