Converging to Gosper's algorithm
TL;DR: A unified approach to computing the universal denominators as given by Gosper's algorithm and Abramov's algorithm for finding rational solutions to linear difference equations with polynomial coefficients is presented.
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About: This article is published in Advances in Applied Mathematics. The article was published on 01 Sep 2008. and is currently open access. The article focuses on the topics: Gosper's algorithm & Polynomial.
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Citations
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Partial denominator bounds for partial linear difference equations
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Concrete Mathematics: A Foundation for Computer Science
Ron Graham,Donald E. Knuth,Oren Patashnik +2 more
- 01 Jan 1994
TL;DR: This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms, and is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it!
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Concrete Mathematics: A Foundation for Computer Science.
TL;DR: Concrete Mathematics as discussed by the authors is a collection of techniques for solving problems in computer science, and it is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline.
2.8K
A holonomic systems approach to special functions identities
TL;DR: In this article, it was shown that any identity involving sums and integrals of products of holonomic functions can be verified in a finite number of steps. But this is partially substantiated by an algorithm that proves terminating hypergeometric series identities, and that is given both in English and in MAPLE.
653
The method of creative telescoping
TL;DR: An algorithm for definite hypergeometric summation is given that is based, in a non-obvious way, on Gosper's algorithm, and its theoretical justification relies on Bernstein's theory of holonomic systems.
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