The C-finite Ansatz Meets the Holonomic Ansatz

Abstract

We show how the continuous Almkvist-Zeilberger algorithm can be used to efficiently discover and prove differential equations satisfied by generating functions of sequences defined as integrals of powers of C-finite polynomial sequences (like the Chebyshev polynomials) from which one can automatically derive linear recurrences with polynomial coefficients for the sequences themselves. We fully implement this with a Maple package, CfiniteIntergal.txt .

4 pages. Accompanied by a Maple package, and sample input and output files available from http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/cfiniteI.html