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authordos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
committerdos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
commitab8cc85adde879fb963c94d15675783f2cf4b183 (patch)
treec202482327f474583b750b2c45dedfc4e4312b1d /src/input/series2.input.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
Initial population.
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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}