construct the regular q-Pochhammer representation of a q-hypergeometric term - Maple Help

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QDifferenceEquations[RegularQPochhammerForm] - construct the regular q-Pochhammer representation of a q-hypergeometric term

Calling Sequence

RegularQPochhammerForm(H, q, n)

Parameters

H

-

q-hypergeometric term of n

q

-

name used as the parameter q, usually q

n

-

variable

Description

• 

Let H be a q-hypergeometric term of q^n, R be the certificate of H, and n0 be an integer such that R has neither a pole nor a zero for all n0n. Let R factor into linear factors

R:=zxa1...xarxb1....xbs

  

The RegularQPochhammerForm(H,q,n) command returns the multiplicative decomposition of the form Hqn0Cwnn0Pn where

P:=QPochhammer1a1,q,n...QPochhammer1ar,q,nQPochhammer1b1,q,n....QPochhammer1bs,q,n

w:=1r+sza1...arb1....bs

C:=qbinomialn,2QPochhammer1b1,q,n0...QPochhammer1bs,q,n0qbinomialn0,2QPochhammer1a1,q,n0....QPochhammer1ar,q,n0

Examples

withQDifferenceEquations:

H:=k=0n1qk+q2qk+1qk+q5q3qk+q4q2q3qk+q21q12qk+q21qk+q5qk+q42q4qk+1qk+q21q2qk+q21

H:=k=0n1qk+q2qk+1qk+q5q3qk+q4q2q3qk+q21q12qk+q21qk+q5qk+q42q4qk+1qk+q21q2qk+q21

(1)

RegularQPochhammerFormH,q,n

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

(2)

See Also

QDifferenceEquations[QEfficientRepresentation], QDifferenceEquations[QMultiplicativeDecomposition], QDifferenceEquations[QRationalCanonicalForm]


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