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arXiv · 1512.06902

The C-finite Ansatz Meets the Holonomic Ansatz

Shalosh B. Ekhad·Doron Zeilberger
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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 .

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Shalosh B. Ekhad, Doron Zeilberger. 2015-12-21. The C-finite Ansatz Meets the Holonomic Ansatz. https://arxiv.org/abs/1512.06902

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