rekurranse

Rekurranse is a term used in Norwegian and Danish to denote the repeating occurrence of events, values, or patterns over time or space. In science and mathematics, rekurranse is commonly associated with recurrence relations, equations that define a sequence where each term is expressed in terms of previous ones, together with initial conditions.

A typical linear recurrence relation of order k has the form a_n = c1 a_{n-1} + c2 a_{n-2} + ... + ck a_{n-k} + f(n). The Fibonacci sequence is the classic example, with a_n = a_{n-1} + a_{n-2} and initial values a_0, a_1. Solutions can be obtained via the characteristic equation, generating functions, or, for large n, asymptotic estimates.

Beyond pure mathematics, rekurranse concepts appear in algorithm design (dynamic programming relies on solving recurrence relations), population models, financial planning (recursive cash flow models), and in the study of disease recurrence, where a condition returns after remission. In geophysics and physics, recurrence describes repeated events such as earthquake recurrence intervals or Poincaré recurrences in dynamical systems. In signal processing and time-series analysis, rekurranse-based methods examine how similar states reappear over a trajectory; recurrence plots visualize this behavior.

Terminology: rekurranse in Scandinavian languages corresponds to the English recurrence; related terms include renewal, repetition, and recurrence time in stochastic processes.