BUILT-IN MATHEMATICA SYMBOL

QBinomial

gives the

-binomial coefficient

.

Exact evaluation with numbers:

Use FunctionExpand to obtain Gaussian polynomials:

Exact evaluation with numbers:

Out[1]=

Out[2]=

Use FunctionExpand to obtain Gaussian polynomials:

Out[1]=

Evaluate numerically:

Evaluate for

:

Evaluate for complex arguments:

Evaluate to arbitrary precision:

The precision of the output tracks the precision of the input:

QBinomial threads element-wise over lists:

QBinomial can be applied to a power series:

Explicit combinatorial construction of QBinomial:

-binomial is a generating function for the sequence in a :

Compare to explicit counting:

Elements in the

-Pascal triangle satisfy two recurrence relations:

The number of subspaces in the

-dimensional vector space over

with prime-power

:

Total number of subspaces in three-dimensional vector space over

:

Check using recurrence equation for Galois numbers:

Use FunctionExpand and FullSimplify to manipulate expressions containing QBinomial:

Build series expansions: