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 $\mathrm{n0}\le n$. Let R factor into linear factors

The RegularQPochhammerForm(H,q,n) command returns the multiplicative decomposition of the form $H\left(q^{\mathrm{n0}}\right)C{w}^{n-\mathrm{n0}}P\left(n\right)$ where

$\mathrm{with}\left(\mathrm{QDifferenceEquations}\right)\:$

$H≔\mathrm{Product}\left(\frac{\left(q^k+q^2\right)\left(q^k+1\right)\left(q^k+q^5-q^3\right)\left(q^k+q^4-q^2\right)\left(q^3{q}^k+q^2-1\right)\left(q^{12}{q}^k+q^2-1\right)}{\left(q^k+q^5\right){\left(q^k+q^4\right)}^2\left(q^4{q}^k+1\right)\left(q^k+q^2-1\right)\left(q^2{q}^k+q^2-1\right)}\,k=0..n-1\right)$

$H≔\prod _{k=0}^{n-1}\frac{\left(q^k+q^2\right)\left(q^k+1\right)\left(q^k+q^5-q^3\right)\left(q^k+q^4-q^2\right)\left(q^3{q}^k+q^2-1\right)\left(q^{12}{q}^k+q^2-1\right)}{\left(q^k+q^5\right){\left(q^k+q^4\right)}^2\left(q^4{q}^k+1\right)\left(q^k+q^2-1\right)\left(q^2{q}^k+q^2-1\right)}$

$\mathrm{RegularQPochhammerForm}\left(H\,q\,n\right)$

$\frac{{\left(\frac{{\left(q^2-1\right)}^2}{q^6}\right)}^n\mathrm{QPochhammer}\left(-\frac{q^3}{q^2-1}\,q\,n\right)\mathrm{QPochhammer}\left(\frac{1}{-q^4+q^2}\,q\,n\right)\mathrm{QPochhammer}\left(-\frac{q^{12}}{q^2-1}\,q\,n\right)\mathrm{QPochhammer}\left(\frac{1}{-q^5+q^3}\,q\,n\right)\mathrm{QPochhammer}\left(\mathrm{-1}\,q\,n\right)\mathrm{QPochhammer}\left(-\frac{1}{q^2}\,q\,n\right)}{\mathrm{QPochhammer}\left(-\frac{q^2}{q^2-1}\,q\,n\right)\mathrm{QPochhammer}\left(-q^4\,q\,n\right){\mathrm{QPochhammer}\left(-\frac{1}{q^4}\,q\,n\right)}^2\mathrm{QPochhammer}\left(-\frac{1}{q^5}\,q\,n\right)\mathrm{QPochhammer}\left(\frac{1}{-q^2+1}\,q\,n\right)}$