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QDifferenceEquations[RegularQPochhammerForm] - construct the regular q-Pochhammer representation of a q-hypergeometric term
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Calling Sequence
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RegularQPochhammerForm(H, q, n)
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Parameters
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H
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q-hypergeometric term of n
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q
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name used as the parameter q, usually q
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n
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variable
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Description
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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  . Let R factor into linear factors
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![R := z*(x-a[1])*`...`*(x-a[r])/((x-b[1])*`....`*(x-b[s]))](/support/helpjp/helpview.aspx?si=8747/file02652/math84.png)
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The RegularQPochhammerForm(H,q,n) command returns the multiplicative decomposition of the form  where
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![P := QPochhammer(1/a[1], q, n)*`...`*QPochhammer(1/a[r], q, n)/(QPochhammer(1/b[1], q, n)*`....`*QPochhammer(1/b[s], q, n))](/support/helpjp/helpview.aspx?si=8747/file02652/math95.png)
![w := (-1)^(r+s)*z*a[1]*`...`*a[r]/(b[1]*`....`*b[s])](/support/helpjp/helpview.aspx?si=8747/file02652/math100.png)
![C := q^binomial(n, 2)*QPochhammer(1/b[1], q, n0)*`...`*QPochhammer(1/b[s], q, n0)/(q^binomial(n0, 2)*QPochhammer(1/a[1], q, n0)*`....`*QPochhammer(1/a[r], q, n0))](/support/helpjp/helpview.aspx?si=8747/file02652/math105.png)
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