Algorithms for definite summation or integration produce a linear recurrence of differential operator with polynomial coefficients as output. These operators are called telescopers. The telescopers for a given summation or integration problem are not unique, so the question arises whether some of them are easier to compute than others. To answer this, we first have to understand the possible sizes of the telescopers. We give an overview over some recent results in this direction. Some of them are joint work with Shaoshi Chen, others are joint work with Lily Yen.
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