## Hypergeometric summation: an algorithmic approach to summation and special function identitiesIn this book modern algorithmic techniques for summation, most of which have been introduced within the last decade, are developed and carefully implemented in the computer algebra system Maple. 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 book. 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 present book is designed for use in the framework of a seminar but is also suitable for an advanced lecture course in this area. |

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### Contents

Introduction | 1 |

Hypergeometric Identities | 11 |

Hypergeometric Database | 31 |

Copyright | |

9 other sections not shown

### Common terms and phrases

1998 Wolfram Koepf Algorithm 10.2 Algorithm 2.1 antiderivative application of Gosper's applied binomial coefficients binomial theorem calculation chapter Chu-Vandermonde identity computation computer algebra system Copyright 1998 Wolfram database deduce degree bound denominator denote equate coefficients equation of order ERROR('algorithm Example Exercise finite support formula g-analogues given Gosper-summable Gosper's algorithm Hence holonomic recurrence equation hyperexponential term Hypergeom hypergeometric function hypergeometric identities hypergeometric representation hypergeometric summation hypergeometric term solutions implementation initial values input integer integer-linear integral Jacobi polynomials Konrad-Zuse-Zentrum Berlin Laguerre polynomials Legendre polynomials Lemma linear system lower parameters Maple procedure nonnegative integer Note option Copyright 1998 order recurrence equation orthogonal polynomials Petkovsek's algorithm Pn(x Pochhammer symbols proof rational certificate rational functions recurrence and differential rewriting right-hand side Rodrigues formula satisfies Session Show sn+i summand term ratio term with respect Theorem valid WZ method Zeilberger Zeilberger's algorithm zero