# 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)
100 years of Dixon’s identity. (English) Zbl 0795.01009

1991 marks the 100th anniversary of the appearance of a note by Alfred Cardew Dixon proving a famous combinatorial identity. The following slight generalisation also bears Dixon’s name:

$\sum _{k}\left(\genfrac{}{}{0pt}{}{a+b}{a+k}\right)\left(\genfrac{}{}{0pt}{}{b+c}{b+k}\right)\left(\genfrac{}{}{0pt}{}{c+a}{c+k}\right){\left(-1\right)}^{k}=\frac{\left(a+b+c\right)!}{a!b!c!}$

for nonnegative integers $a,b,c$ and the permitted range of the integer $k$. In the paper we can find three proofs of Dixon’s identity, namely Dixon’s original proof, a second proof using the Lagrange inversion formula, and a third one using WZ pairs. From the paper we can learn some biographical facts about Dixon who was the President of the London Mathematical Society in 1931-33.

##### MSC:
 01A55 Mathematics in the 19th century 05A10 Combinatorial functions
##### Keywords:
combinatorial identity; binomial coefficients