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Title: Gosper's Algorithm -- from Wolfram MathWorld

Open Graph Title: Gosper's Algorithm -- from Wolfram MathWorld

X Title: Gosper's Algorithm -- from Wolfram MathWorld

Description: An algorithm for finding closed form hypergeometric identities. The algorithm treats sums whose successive terms have ratios which are rational functions. Not only does it decide conclusively whether there exists a hypergeometric sequence z_n such that t_n=z_(n+1)-z_n, (1) but actually produces z_n if it exists. If not, it produces sum_(k=0)^(n-1)t_k. An outline of the algorithm follows (Petkovšek et al. 1996): 1. For the ratio r(n)=t_(n+1)/t_n which is a rational function of n. ...

Open Graph Description: An algorithm for finding closed form hypergeometric identities. The algorithm treats sums whose successive terms have ratios which are rational functions. Not only does it decide conclusively whether there exists a hypergeometric sequence z_n such that t_n=z_(n+1)-z_n, (1) but actually produces z_n if it exists. If not, it produces sum_(k=0)^(n-1)t_k. An outline of the algorithm follows (Petkovšek et al. 1996): 1. For the ratio r(n)=t_(n+1)/t_n which is a rational function of n. ...

X Description: An algorithm for finding closed form hypergeometric identities. The algorithm treats sums whose successive terms have ratios which are rational functions. Not only does it decide conclusively whether there exists a hypergeometric sequence z_n such that t_n=z_(n+1)-z_n, (1) but actually produces z_n if it exists. If not, it produces sum_(k=0)^(n-1)t_k. An outline of the algorithm follows (Petkovšek et al. 1996): 1. For the ratio r(n)=t_(n+1)/t_n which is a rational function of n. ...

Opengraph URL: https://mathworld.wolfram.com/GospersAlgorithm.html

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direct link

Domain: mathworld.wolfram.com

DC.TitleGosper's Algorithm
DC.CreatorWeisstein, Eric W.
DC.DescriptionAn algorithm for finding closed form hypergeometric identities. The algorithm treats sums whose successive terms have ratios which are rational functions. Not only does it decide conclusively whether there exists a hypergeometric sequence z_n such that t_n=z_(n+1)-z_n, (1) but actually produces z_n if it exists. If not, it produces sum_(k=0)^(n-1)t_k. An outline of the algorithm follows (Petkovšek et al. 1996): 1. For the ratio r(n)=t_(n+1)/t_n which is a rational function of n. ...
DC.Subject33C
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/GospersAlgorithm.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
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og:typewebsite
twitter:cardsummary_large_image
twitter:image:srchttps://mathworld.wolfram.com/images/socialmedia/share/ogimage_GospersAlgorithm.png
Noneie=edge

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hypergeometric identitieshttps://mathworld.wolfram.com/HypergeometricIdentity.html
rational functionshttps://mathworld.wolfram.com/RationalFunction.html
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Zeilberger's algorithmhttps://mathworld.wolfram.com/ZeilbergersAlgorithm.html
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Concrete Mathematics: A Foundation for Computer Science, 2nd ed.http://www.amazon.com/exec/obidos/ASIN/0201558025/ref=nosim/ericstreasuretro
Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities.http://www.amazon.com/exec/obidos/ASIN/3528069503/ref=nosim/ericstreasuretro
Computer Algebra Symbolic and Algebraic Computation, 2nd ed.http://www.amazon.com/exec/obidos/ASIN/038781776X/ref=nosim/ericstreasuretro
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https://www2.math.upenn.edu/~wilf/AeqB.htmlhttps://www2.math.upenn.edu/~wilf/AeqB.html
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