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Statements

Subject Item
dbr:Recurrence_relation
dbo:wikiPageWikiLink
dbr:P-recursive_equation
Subject Item
dbr:Abramov's_algorithm
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P-recursive equation
rdfs:comment
In mathematics a P-recursive equation is a linear equation of sequences where the coefficient sequences can be represented as polynomials. P-recursive equations are linear recurrence equations (or linear recurrence relations or linear difference equations) with polynomial coefficients. These equations play an important role in different areas of mathematics, specifically in combinatorics. The sequences which are solutions of these equations are called holonomic, P-recursive or D-finite.
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1058066069
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dbr:Formal_power_series dbr:Hypergeometric_identity dbr:System_of_linear_equations dbr:Sequence_space dbr:Marko_Petkovšek dbr:Doron_Zeilberger dbr:Combinatorics dbr:Field_of_characteristic_zero dbr:Basis_(linear_algebra) dbc:Polynomials dbr:Involution_(mathematics) dbr:Rational_function dbr:Algebraic_closure dbr:Petkovšek's_algorithm dbr:Polynomial_ring dbr:Sequence dbr:Gamma_function dbr:Kernel_(linear_algebra) dbr:Generalized_permutation_matrix dbr:Holonomic_function
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In mathematics a P-recursive equation is a linear equation of sequences where the coefficient sequences can be represented as polynomials. P-recursive equations are linear recurrence equations (or linear recurrence relations or linear difference equations) with polynomial coefficients. These equations play an important role in different areas of mathematics, specifically in combinatorics. The sequences which are solutions of these equations are called holonomic, P-recursive or D-finite. From the late 1980s on the first algorithms were developed to find solutions for these equations. Sergei A. Abramov, Marko Petkovšek and Mark van Hoeij described algorithms to find polynomial, rational, hypergeometric and d'Alembertian solutions.
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