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  2. Linear recurrence with constant coefficients - Wikipedia

    en.wikipedia.org/wiki/Linear_recurrence_with...

    In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients [1]: ch. 17 [2]: ch. 10 (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence.

  3. Polynomial solutions of P-recursive equations - Wikipedia

    en.wikipedia.org/wiki/Polynomial_solutions_of_P...

    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. [1] [2] The algorithm computes a degree bound for the solution in a first step.

  4. Kleene's recursion theorem - Wikipedia

    en.wikipedia.org/wiki/Kleene's_recursion_theorem

    For example, consider the set of recursion equations: = (+) = = There is no function g satisfying these equations, because they imply g(2) = 1 and also imply g(2) = 0. Thus there is no fixed point g satisfying these recursion equations. It is possible to make an enumeration operator corresponding to these equations, but it will not be a ...

  5. P-recursive equation - Wikipedia

    en.wikipedia.org/wiki/P-recursive_equation

    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.

  6. Recursion - Wikipedia

    en.wikipedia.org/wiki/Recursion

    Recursion in computer programming is exemplified when a function is defined in terms of simpler, often smaller versions of itself. The solution to the problem is then devised by combining the solutions obtained from the simpler versions of the problem. One example application of recursion is in parsers for programming languages. The great ...

  7. Constant-recursive sequence - Wikipedia

    en.wikipedia.org/wiki/Constant-recursive_sequence

    The equation is called a linear recurrence relation. The concept is also known as a linear recurrence sequence, linear-recursive sequence, linear-recurrent sequence, or a C-finite sequence. [1] For example, the Fibonacci sequence,,,,, …,

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