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diff --git a/src/input/infprod.input.pamphlet b/src/input/infprod.input.pamphlet new file mode 100644 index 00000000..74121fc0 --- /dev/null +++ b/src/input/infprod.input.pamphlet @@ -0,0 +1,64 @@ +\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} |