TOPICS
Search

Quadratic Recurrence Equation

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook

A quadratic recurrence is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a second-degree polynomial in x_k with k<n. For example,

x_n=x_(n-1)x_(n-2)

is a quadratic recurrence equation.

A quadratic recurrence equation of the form

x_n=ax_(n-1)^2+bx_(n-1)+c

in which no cross terms are present is known as a quadratic map.

See also

Julia Set, Linear Recurrence Equation, Logistic Map, Mandelbrot Set, Quadratic Map, Recurrence Equation, Sylvester's Sequence

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Quadratic Recurrence Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/QuadraticRecurrenceEquation.html

Subject classifications