Parameterized Telescoping Proves Algebraic Independence of Sums

Details Parameterized Telescoping Proves Algebraic Independence of Sums Parameterized Telescoping Proves Algebraic Independence of Sums

2008-08-19

arxiv.org/abs/0808.2596v1

Computer Science

Symbolic Computation

To appear in Annals of Combinatorics

Scientific paper

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, e.g., Zeilberger's algorithm fails to find a recurrence with minimal order.

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