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QBinomial

QBinomial
gives the -binomial coefficient .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • .
Exact evaluation with numbers:
Use FunctionExpand to obtain Gaussian polynomials:
Exact evaluation with numbers:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
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Use FunctionExpand to obtain Gaussian polynomials:
In[1]:=
Click for copyable input
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:
TraditionalForm formatting:
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:
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