Develop Computer Programs for Simplifying Sums That Involve Binomial Coe Cients

By Knuth, Donald E.

Book Id: WPLBN0000661347
Format Type: PDF eBook
File Size: 1.19 MB
Reproduction Date: 2005

Title:	Develop Computer Programs for Simplifying Sums That Involve Binomial Coe Cients
Author:	Knuth, Donald E.
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Language:	English
Subject:	Science., Mathematics, Logic
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Citation APA MLA Chicago Knuth, D. E. (n.d.). Develop Computer Programs for Simplifying Sums That Involve Binomial Coe Cients. Retrieved from http://gutenberg.us/

Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: Some entries in the hypergeometric database. Using the database. Is there really a hypergeometric database?...

Table of Contents
Contents Foreword vii A Quick Start : : : ix I Background 1 1 Proof Machines 3 1.1 Evolution of the province of human thought . . . . . . . . . . . . . . 3 1.2 Canonical and normal forms . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Polynomial identities . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Proofs by example? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Trigonometric identities . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.6 Fibonacci identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.7 Symmetric function identities . . . . . . . . . . . . . . . . . . . . . . 12 1.8 Elliptic function identities . . . . . . . . . . . . . . . . . . . . . . . . 13 2 Tightening the Target 17 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 Human and computer proofs; an example . . . . . . . . . . . . . . . . 23 2.4 AMathematica session . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.5 AMaple session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.6 Where we are and what happens next . . . . . . . . . . . . . . . . . . 30 2.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3 The Hypergeometric Database 33 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Hypergeometric series . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3 How to identify a series as hypergeometric . . . . . . . . . . . . . . . 35 3.4 Software that identi?es hypergeometric series . . . . . . . . . . . . . . 39