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We consider linear systems of recurrence equations whose coefficients aregiven in terms of indefinite nested sums and products covering, e.g., theharmonic numbers, hypergeometric products, $q$-hypergeometric products or theirmixed versions. These linear systems are formulated in the setting of$\Pi\Sigma$-extensions and our goal is to find a denominator bound (also knownas 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 isthe first step in computing all rational solutions of such a rather generalrecurrence system. Once the denominator bound is known, the problem of solvingfor rational solutions is reduced to the problem of solving for polynomialsolutions.

Denominator Bounds for Systems of Recurrence Equations using $\Pi\Sigma$-Extensions