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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input series2.input}
\author{Clifton J. Williamson}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{License}
<<license>>=
--Copyright The Numerical Algorithms Group Limited 1994.
@
<<*>>=
<<license>>
--% Expression To Power Series
-- We compute series expansions of various functions using EXPR2UPS and STTF.
-- Author: Clifton J. Williamson
-- Date Created: 12 August 1992
-- Date Last Updated: 12 August 1992
-- Keywords: Taylor series
-- References:
-- Power series expansions around branch points
-- (Well not really, since we have x**2, not x. Otherwise, our series
-- expansions would have fractional powers.)
f1 := taylor(1 - x**2,x = 0)
asin f1
sin %
acos f1
cos %
f2 := taylor(1 + x**2,x = 0)
acsc f2
csc %
asec f2
sec %
f3 := taylor(1 - (x - a)**2,x = a)
asin f3
sin %
acos f3
cos %
f4 := taylor(1 + (x - a)**2,x = a)
acsc f4
csc %
asec f4
sec %
f5 := taylor(%i + x**2,x = 0)
asinh f5
map(normalize,sinh %)
acosh f1
map(normalize,cosh %)
asech f2
sech %
acsch f1
map(normalize,csch %)
f6 := taylor(%i + (x - a)**2,x = a)
asinh f6
map(normalize,sinh %)
acosh f3
map(normalize,cosh %)
asech f4
sech %
acsch f3
map(normalize,csch %)
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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