zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
$A=B$. With foreword by Donald E. Knuth. (English) Zbl 0848.05002
Wellesley, MA: A. K. Peters. xii, 212 p. $ 39.00 (1996).
This book is an essential resource for anyone who ever encounters binomial coefficient identities, for anyone who is interested in how computers are being used to discover and prove mathematical identities, and for anyone who simply enjoys a well-written book that presents interesting, cutting edge mathematics in an accessible style. Wilf and Zeilberger have been at the forefront of a group of researchers who have found and implemented algorithmic approaches to the study of identities for hypergeometric and basic hypergeometric series. In this book, they detail where to find the packages that implement these algorithms in either Maple or Mathematica, they give examples of and instructions in how to use these packages, and they explain the motivation and theory behind the algorithms. The specific algorithms that are described are Sister Celine’s Method, an algorithm from the 1940’s that underlies most of the current research; Gosper’s Algorithm, the first of the powerful proof techniques to be implemented with a computer algebra package; Zeilberger’s Algorithm which extends and generalizes Gosper’s approach; the WZ Method which is guaranteed to provide a proof certificate for any correct identity for hypergeometric series and which can be used to determine whether or not a “closed form” exists for any given hypergeometric series. The book is also sprinkled with examples, exercises, and elaborations on the ideas that come into play.

05A10Combinatorial functions
05A30$q$-calculus and related topics
33C20Generalized hypergeometric series, ${}_pF_q$
68R05Combinatorics in connection with computer science
33D15Basic hypergeometric functions of one variable, ${}_r\phi_s$
39A70Difference operators
Maple; Mathematica