zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Pfaff’s method. II: Diverse applications. (English) Zbl 0862.33003
The paper discusses Pfaff’s proof of the Saalschütz summation, which actually preceded Saalschütz’ work by hundred years. Set S n (a,b,c)= 3 F 2 -n,a,b;1 c,1+a+b-c-n, and σ n (a,b,c)=(c-a) n (c-b) n (c) n (c-a-b) n . The Saalschütz summation states S n (a,b,c)=σ n (a,b,c), and Pfaff proved it in the simplest possible way: showed that S n (a,b,c)-S n-1 (a,b,c) and σ n (a,b,c)-σ n-1 (a,b,c) admit the same recurrence. This Pfaffian approach is shown to be effective for Bailey’s, Dougall’s, Lakin’s and Kummer’s summation identities. It is noted that the Pfaffian approach seems most effective for balanced and well-poised hypergeometric series. It is often the case that the Pfaffian approach has to prove a cluster of related identities, and not just one of them.

MSC:
33C20Generalized hypergeometric series, p F q
05A19Combinatorial identities, bijective combinatorics