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QDifferenceEquations

  

QSimpComb

  

simplification of expressions involving q-hypergeometric terms

  

QSimplify

  

simplification of expressions involving q-hypergeometric terms

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

QSimpComb(f)

QSimplify(f)

Parameters

f

-

algebraic expression

Description

• 

The commands QSimpComb and QSimplify are for simplification of expressions involving q-hypergeometric terms. For a function fqk, the main use of QSimpComb is for detecting if fqk is a q-hypergeometric term in qk. That is, if fqk+1fqk is a rational function in qk (see IsQHypergeometricTerm). If the result is not a rational function, QSimplify returns in general a more compact answer.

• 

This implementation is mainly based on the implementation by H. Boeing, W. Koepf. See the Reference Section.

Examples

withQDifferenceEquations:

Hq212q6nQPochhammer1q5+q3,q,nQPochhammer1q4+q2,q,nQPochhammer1q3q21,q,nQPochhammer1q2,q,nQPochhammer1q12q21,q,nQPochhammer1,q,nQPochhammer1q2q21,q,nQPochhammer1q5,q,nQPochhammer1q4,q,n2QPochhammerq4,q,nQPochhammer1q2+1,q,n

H:=q212q6nQDifferenceEquations:-QPochhammer1q5+q3,q,nQDifferenceEquations:-QPochhammer1q4+q2,q,nQDifferenceEquations:-QPochhammerq3q21,q,nQDifferenceEquations:-QPochhammer1q2,q,nQDifferenceEquations:-QPochhammerq12q21,q,nQDifferenceEquations:-QPochhammer1,q,nQDifferenceEquations:-QPochhammerq2q21,q,nQDifferenceEquations:-QPochhammer1q5,q,nQDifferenceEquations:-QPochhammer1q4,q,n2QDifferenceEquations:-QPochhammerq4,q,nQDifferenceEquations:-QPochhammer1q2+1,q,n

(1)

Apply QSimpComb to the consecutive ratio Hn+1Hn. If the result is a rational function in qn, then H is a q-hypergeometric term.

QSimpCombsubsn=n+1,HH

q5q3+qnq2+qn1+qnqnq12+q21qnq3+q21q4q2+qnq2qn+q21q2+qn1q4+qn21+qnq4q5+qn

(2)

IsQHypergeometricTermH,n,qn=N

true

(3)

fQPochhammeraqkn,q,nQPochhammerqa,q,knanqbinomialn,2kn2QPochhammerqa,q,knn

f:=QDifferenceEquations:-QPochhammeraqkn,q,nQDifferenceEquations:-QPochhammerqa,q,knanqbinomialn,2kn2QDifferenceEquations:-QPochhammerqa,q,knn

(4)

QSimplifyf

0

(5)

f1QPochhammera,q2,nQPochhammeraq,q2,nQPochhammera,q,2n

f:=QDifferenceEquations:-QPochhammera,q2,nQDifferenceEquations:-QPochhammerqa,q2,nQDifferenceEquations:-QPochhammera,q,2n

(6)

QSimpCombf

QDifferenceEquations:-QPochhammera,q2,nQDifferenceEquations:-QPochhammerqa,q2,nQDifferenceEquations:-QPochhammera,q,2n

(7)

QSimplifyf

1

(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[QObjects]

 


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