author = {C. Schneider},
title = {{Refined telescoping algorithms in $R\Pi\Sigma$-extensions to reduce the degrees of the denominators}},
language = {english},
abstract = {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 $R\Pi\Sigma$-ring extensions that are built over general $\Pi\Sigma$-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.},
number = {23-01},
year = {2023},
month = {February},
note = {arXiv:2302.03563 [cs.SC]},
keywords = {telescoping, difference rings, reduced denominators, nested sums},
length = {18},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}