A solvable nonlinear autonomous recursion of arbitrary order

Abstract

The initial-values problem of the following nonlinear autonomous recursion of order p , z (s + p) = c product of [z (s + l)]^a_l ; with p an arbitrary positive integer, z (s) the dependent variable (possibly a complex number), s the independent variable (a non negative integer), c an arbitrarily assigned, possibly complex, number, and the p exponents a_l arbitrarily assigned integers (positive, negative or vanishing, so that the right-hand side of the recursion be univalent)|is solvable by algebraic operations, involving the solution of a system of linear algebraic equations (generally explicitly solvable) and of a single polynomial equation of degree p (hence explicitly solvable for p = 1; 2; 3; 4 ).

7 pages

References in corpus (4)

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• Explicitly Solvable Systems of First-Order Difference Equations With Homogeneous Polynomial Right-Hand Sides
• Two classes of explicitly solvable sextic equations
• Explicitly solvable algebraic equations of degree 8 and 9