P-recursive equation

<p>In mathematics a P-recursive equation is a <a href="/facts/Linear_equation/JfCgALwf">linear equation</a> of <a href="/facts/Sequence/gV2S4uqp">sequences</a> where the coefficient sequences can be represented as <a href="/facts/Polynomial_ring/ua3vk8Ih">polynomials</a>. P-recursive equations are linear <a href="/facts/Recurrence_equation/JolXC71M">recurrence equations</a> (or linear recurrence relations or linear difference equations) with polynomial coefficients. These equations play an important role in different areas of mathematics, specifically in <a href="/facts/Combinatorics/k14xUoKT">combinatorics</a>. The sequences which are solutions of these equations are called <a href="/facts/Holonomic_function/eaVU0RNs">holonomic</a>, P-recursive or D-finite.
</p><p>From the late 1980s, the first algorithms were developed to find solutions for these equations. Sergei A. Abramov, <a href="/facts/Marko_Petkov%C5%A1ek/xSEcWwv1">Marko Petkovšek</a> and Mark van Hoeij described algorithms to find polynomial, rational, hypergeometric and d'Alembertian solutions.
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P-recursive equation open-in-new

P-recursive equation