Refined telescoping algorithms in RΠΣ-extensions to reduce the degrees of the denominators

02/07/2023

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by   Carsten Schneider, et al.

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We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The underlying (parameterized) telescoping algorithms can be executed in RΠΣ-ring extensions that are built over general ΠΣ-fields. An important application of this toolbox is the simplification of d'Alembertian and Liouvillian solutions coming from recurrence relations where the denominators of the arising sums do not factor nicely.