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arXiv · 1402.2409

A Generalized Apagodu-Zeilberger Algorithm

Shaoshi Chen·Manuel Kauers·Christoph Koutschan
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Abstract

The Apagodu-Zeilberger algorithm can be used for computing annihilating operators for definite sums over hypergeometric terms, or for definite integrals over hyperexponential functions. In this paper, we propose a generalization of this algorithm which is applicable to arbitrary $\partial$-finite functions. In analogy to the hypergeometric case, we introduce the notion of proper $\partial$-finite functions. We show that the algorithm always succeeds for these functions, and we give a tight a priori bound for the order of the output operator.

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Shaoshi Chen, Manuel Kauers, Christoph Koutschan. 2014-02-11. A Generalized Apagodu-Zeilberger Algorithm. https://doi.org/10.1145/2608628.2608641

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