Given quantities , , …, , the Gaussian bracket is defined as the sum of all the following terms:[more]
- the product ,
- all products that omit one pair of terms with consecutive indices,
- all products that omit two pairs of terms, each with consecutive indices,
- all products that omit three pairs of terms, each with consecutive indices,
- and so forth, where the empty product has the value 1 if is even.[less]
This term was actually introduced by Euler, who used the notation . Euler or Gauss brackets have applications in number theory, combinatorics, etc.
(The first author was supported by project 1ET200300529 of the Information Society of the National Research Program of the Czech Republic and by the Institutional Research Plan AV0Z10300504; the Demonstration was submitted 2008-04-29.)