Hypergeometric summation. An algorithmic approach to summation and special function identities

✍ Scribed by Koepf W.

• Publisher: Vieweg
• Year: 1998
• Tongue: English
• Leaves: 239
• Series: Viewed Advanced Lectures in Mathematics Series
• Category: Library

✦ Synopsis

In this book, modern algorithmic techniques for summation--most of which have been introduced within the last decade--are developed and carefully implemented via computer algebra system software (which can be downloaded from the Web; URL is given in the text). The algorithms of Gosper, Zeilberger, and Petkovsek on hypergeometric summation and recurrence equations and their $q$-analogues are covered, and similar algorithms on differential equations are considered. An equivalent theory of hyperexponential integration due to Almkvist and Zeilberger completes the volume. The combination of all results considered gives work with orthogonal polynomials and (hypergeometric type) special functions a solid algorithmic foundation. Hence, many examples from this very active field are given. The book is designed for use as framework for a seminar on the topic, but is also suitable for use in an advanced lecture course.

✦ Table of Contents

Contents......Page all_28121_to_00238.cpc0007.djvu
Preface......Page all_28121_to_00238.cpc0003.djvu
Introduction......Page all_28121_to_00238.cpc0009.djvu
1 The Gamma Function......Page all_28121_to_00238.cpc0012.djvu
Exercises......Page all_28121_to_00238.cpc0017.djvu
2 Hypergeometric Identities......Page all_28121_to_00238.cpc0019.djvu
q-Hypergeometric Identities......Page all_28121_to_00238.cpc0033.djvu
Exercises......Page all_28121_to_00238.cpc0034.djvu
3 Hypergeometric Database......Page all_28121_to_00238.cpc0039.djvu
q-Hypergeometric Database......Page all_28121_to_00238.cpc0048.djvu
Exercises......Page all_28121_to_00238.cpc0049.djvu
4 Holonomic Recurrence Equations......Page all_28121_to_00238.cpc0052.djvu
Multiple Summation......Page all_28121_to_00238.cpc0062.djvu
q-Holonomic Recurrence Equations......Page all_28121_to_00238.cpc0063.djvu
Exercises......Page all_28121_to_00238.cpc0065.djvu
5 Gosper's Algorithm......Page all_28121_to_00238.cpc0069.djvu
Linearization of Gosper's Algorithm......Page all_28121_to_00238.cpc0082.djvu
Exercises......Page all_28121_to_00238.cpc0083.djvu
6 The Wilf-Zeilberger Method......Page all_28121_to_00238.cpc0088.djvu
Exercises......Page all_28121_to_00238.cpc0098.djvu
7 Zeilberger's Algorithm......Page all_28121_to_00238.cpc0101.djvu
Exercises......Page all_28121_to_00238.cpc0121.djvu
8 Extensions of the Algorithms......Page all_28121_to_00238.cpc0132.djvu
Exercises......Page all_28121_to_00238.cpc0146.djvu
9 Petkovsek's Algorithm......Page all_28121_to_00238.cpc0148.djvu
Exercises......Page all_28121_to_00238.cpc0166.djvu
10 Differential Equations for Sums......Page all_28121_to_00238.cpc0172.djvu
q-Differential Equations for Sums......Page all_28121_to_00238.cpc0184.djvu
Exercises......Page all_28121_to_00238.cpc0186.djvu
11 Hyperexponential Antiderivatives......Page all_28121_to_00238.cpc0191.djvu
Exercises......Page all_28121_to_00238.cpc0200.djvu
12 Holonomic Equations for Integrals......Page all_28121_to_00238.cpc0202.djvu
Exercises......Page all_28121_to_00238.cpc0211.djvu
13 Rodrigues Formulas and Generating Functions......Page all_28121_to_00238.cpc0215.djvu
Exercises......Page all_28121_to_00238.cpc0219.djvu
Appendix: Installation of the Software......Page all_28121_to_00238.cpc0222.djvu
Bibliography......Page all_28121_to_00238.cpc0224.djvu
List of Symbols......Page all_28121_to_00238.cpc0232.djvu
Index......Page all_28121_to_00238.cpc0233.djvu