Parameterized Telescoping Proves Algebraic Independence of Sums
By Carsten Schneider. arXiv.org, 2008
398 citations recorded by the source corpus.
Usually creative telescoping is used to derive recurrences for sums. In this article we show that the non-existence of a creative telescoping solution, and more generally, of a parameterized telescoping solution, proves algebraic independence of certain types of sums. Combining this fact with summation-theory shows transcendence of whole classes of sums. Moreover, this result throws new light on the question why, for example, Zeilberger’s algorithm fails to find a recurrence with minimal order.
Subfields: Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/c4bbad3c9a8bc1dbf446692d44c231997ceb96c4
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