Maple Package CfiniteIntegral.txt, Finds recurrences for sequences defined by integrals of powers of sequences of families of polynomials in x (like the Chebyshev) that satisfy a linear recurrence equation with coefficients that are polynomials in x (but do not depend on the index n). See arxiv-article: The C-finite Ansatz Meets the Holonomic Ansatz. 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 .

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  1. Shalosh B. Ekhad, Doron Zeilberger: The C-finite Ansatz Meets the Holonomic Ansatz (2015) arXiv