Denominator Bounds for Systems of Recurrence Equations Using $$\varPi \varSigma $$-Extensions

We consider linear systems of recurrence equations whose coefficients are given in terms of indefinite nested sums and products covering, e.g., the harmonic numbers, hypergeometric products, q-hypergeometric products or their mixed versions. These linear systems are formulated in the setting of \(\varPi \varSigma \)-extensions and our goal is to find a denominator bound (also known as universal denominator) for the solutions; i.e., a non-zero polynomial d such that the denominator of every solution of the system divides d. This is the first step in computing all rational solutions of such a rather general recurrence system. Once the denominator bound is known, the problem of solving for rational solutions is reduced to the problem of solving for polynomial solutions.