From ab8cc85adde879fb963c94d15675783f2cf4b183 Mon Sep 17 00:00:00 2001
From: dos-reis <gdr@axiomatics.org>
Date: Tue, 14 Aug 2007 05:14:52 +0000
Subject: Initial population.

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 src/input/infprod.input.pamphlet | 64 ++++++++++++++++++++++++++++++++++++++++
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diff --git a/src/input/infprod.input.pamphlet b/src/input/infprod.input.pamphlet
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input infprod.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1991.
+@
+<<*>>=
+<<license>>
+
+--% Infinite products of Taylor series
+-- We compute series expansions of various infinite products using INFPROD0
+-- Author: Clifton J. Williamson
+-- Date Created: 20 August 1992
+-- Date Last Updated: 20 August 1992
+-- Keywords: Taylor series, infinite product
+-- References:
+
+)clear all
+
+-- the partition function
+
+f : UTS(INT,x,0) := 1 - x
+g : UTS(INT,x,0) := recip f
+
+-- the coefficient of x ** n in the following series is the number of ways
+-- that n can be partitioned as a sum of positive integers:
+
+infiniteProduct g
+
+-- Ramanujan's tau function
+
+h := infiniteProduct(f ** 24)
+
+-- the coefficient of x ** n in the following series is Ramanujan's
+-- function tau(n)
+
+delta := x * h
+
+-- the function tau(n) is multiplicative, i.e. if gcd(m,n) = 1, then
+-- tau(m * n) = tau(m) * tau(n)
+
+coefficient(delta,21)
+coefficient(delta,3) * coefficient(delta,7)
+
+coefficient(delta,20)
+coefficient(delta,4) * coefficient(delta,5)
+
+coefficient(delta,65)
+coefficient(delta,13) * coefficient(delta,5)
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
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