Parameterized Telescoping Proves Algebraic Independence of Sums

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.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Carsten Schneider
• Keywords: CORR 2008, Creative Telescoping Solution, Education, Sums, Telescoping Solution