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Statements

Subject Item
dbr:Recurrence_relation
dbo:wikiPageWikiLink
dbr:Polynomial_solutions_of_P-recursive_equations
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dbr:Abramov's_algorithm
dbo:wikiPageWikiLink
dbr:Polynomial_solutions_of_P-recursive_equations
Subject Item
dbr:Polynomial_solutions_of_P-recursive_equations
rdfs:label
Polynomial solutions of P-recursive equations
rdfs:comment
In mathematics a P-recursive equation can be solved for polynomial solutions. Sergei A. Abramov in 1989 and Marko Petkovšek in 1992 described an algorithm which finds all polynomial solutions of those recurrence equations with polynomial coefficients. The algorithm computes a degree bound for the solution in a first step. In a second step an ansatz for a polynomial of this degree is used and the unknown coefficients are computed by a system of linear equations. This article describes this algorithm.
dcterms:subject
dbc:Polynomials
dbo:wikiPageID
58006785
dbo:wikiPageRevisionID
1032161767
dbo:wikiPageWikiLink
dbr:Petkovšek's_algorithm dbr:Falling_and_rising_factorials dbr:Abramov's_algorithm dbr:Marko_Petkovšek dbr:Algorithm dbr:Polynomial_ring dbc:Polynomials dbr:Formal_power_series dbr:Field_(mathematics) dbr:Ansatz dbr:System_of_linear_equations dbr:P-recursive_equation
owl:sameAs
n11:5HdsC wikidata:Q56291989
dbo:abstract
In mathematics a P-recursive equation can be solved for polynomial solutions. Sergei A. Abramov in 1989 and Marko Petkovšek in 1992 described an algorithm which finds all polynomial solutions of those recurrence equations with polynomial coefficients. The algorithm computes a degree bound for the solution in a first step. In a second step an ansatz for a polynomial of this degree is used and the unknown coefficients are computed by a system of linear equations. This article describes this algorithm. In 1995 Abramov, Bronstein and Petkovšek showed that the polynomial case can be solved more efficiently by considering power series solution of the recurrence equation in a specific power basis (i.e. not the ordinary basis ). Other algorithms which compute rational or hypergeometric solutions of a linear recurrence equation with polynomial coefficients also use algorithms which compute polynomial solutions.
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wikipedia-en:Polynomial_solutions_of_P-recursive_equations?oldid=1032161767&ns=0
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7515
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wikipedia-en:Polynomial_solutions_of_P-recursive_equations
Subject Item
dbr:Petkovšek's_algorithm
dbo:wikiPageWikiLink
dbr:Polynomial_solutions_of_P-recursive_equations
Subject Item
wikipedia-en:Polynomial_solutions_of_P-recursive_equations
foaf:primaryTopic
dbr:Polynomial_solutions_of_P-recursive_equations