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单词 GaussianPolynomials
释义

Gaussian polynomials


For an indeterminate q and integers nm0we define the following:

(a) (m)q=qm-1+qm-2++1 for m>0,

(b) (m!)q=(m)q(m-1)q(1)q for m>0, and (0!)q=1,

(c) (nm)q=(n!)q(m!)q((n-m)!)q.If m>n then we define (nm)q=0.

The expressions (nm)q are calledq-binomial coefficientsMathworldPlanetmath or Gaussian polynomials.

Note: if we replace q with 1, then we obtain the familiar integers, factorialsMathworldPlanetmath, and binomial coefficients. Specifically,

(a) (m)1=m,

(b) (m!)1=m!,

(c) (nm)1=(nm).

(d) (mm)q=1.

TitleGaussian polynomials
Canonical nameGaussianPolynomials
Date of creation2013-03-22 11:49:49
Last modified on2013-03-22 11:49:49
Ownermathcam (2727)
Last modified bymathcam (2727)
Numerical id10
Authormathcam (2727)
Entry typeDefinition
Classificationmsc 05A30
Classificationmsc 05A10
Classificationmsc 16S36
Classificationmsc 26A09
Classificationmsc 26A18
Classificationmsc 15A04
Synonymq-binomial coefficients
Related topicContentOfPolynomial
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