Polynomials

Polynomial solutions of P-recursive equations

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. (Wikipedia).

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From playlist Differential Equations

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From playlist Linear Differential Equations

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From playlist Applied Cryptography

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From playlist Series Solutions for Differential Equations

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From playlist Series Solutions for Differential Equations

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From playlist Basics: Differential Equations

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From playlist Differential Equations with YouTube Examples

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Related pages

Petkovšek's algorithm | Ansatz | Falling and rising factorials | System of linear equations | Formal power series | Field (mathematics) | P-recursive equation | Polynomial ring | Algorithm | Abramov's algorithm