QBinomial - Maple Help
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QDifferenceEquations

  

QPochhammer

  

q-Pochhammer symbol

  

QBinomial

  

q-binomial coefficient

  

QBrackets

  

q-brackets

  

QFactorial

  

q-factorial

  

QGAMMA

  

q-Gamma

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

QPochhammer(a, q, infinity)

QPochhammer(a, q, k)

QBinomial(n, k, q)

QBrackets(k, q)

QFactorial(k, q)

QGAMMA(a, q)

Parameters

a

-

algebraic expression

q

-

name used as the parameter q, or an integer power of a name

k

-

symbolic integer value

n

-

symbolic integer value

Description

• 

The QDifferenceEquations package supports five q-hypergeometric terms. They are q-Pochhammer symbol, q-binomial coefficient, q-brackets, q-factorial, and q-Gamma, which correspond to the five functions QPochhammer, QBinomial, QBrackets, QFactorial, and QGAMMA.

• 

These functions are placeholders for the q-objects. The command expand allows expansion of these objects. The command  allows the re-write of QBinomial, QBrackets, QFactorial, and QGAMMA in terms of QPochhammer symbols.

• 

The five q-hypergeometric objects are defined as follows.

  

Note that  (the compact Gasper and Rahman notation) means .

• 

The commands QSimpComb and QSimplify are for simplification of expressions involving these q-objects.

• 

This implementation is mainly based on the implementation by H. Boeing, W. Koepf. See the References section.

Examples

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Compute the certificate of H (which is a rational function in ):

(8)

References

  

Boeing, H., and Koepf, W. "Algorithms for q-hypergeometric summation in computer algebra." Journal of Symbolic Computation. Vol. 11. (1999): 1-23.

See Also

QDifferenceEquations[IsQHypergeometricTerm]

QDifferenceEquations[QSimpComb]

 


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