Explore: Recurrence Relation

In mathematics, a recurrence relation is an equation according to which the n {\displaystyle n} th term of a sequence of numbers is equal to some combination

linear three-term recurrence relation (TTRR, the qualifiers "homogeneous linear" are usually taken for granted) is a recurrence relation of the form y n

and dynamical systems), a linear recurrence with constant coefficients (also known as a linear recurrence relation or linear difference equation) sets

entries would all be 0. Stirling numbers of the second kind obey the recurrence relation (first discovered by Masanobu Saka in his 1782 Sanpō-Gakkai): { n

sequence of probabilist's Hermite polynomials also satisfies the recurrence relation He n + 1 ⁡ ( x ) = x He n ⁡ ( x ) − He n ′ ⁡ ( x ) . {\displaystyle

applications of the recurrence relation. The Fibonacci sequence is a simple classical example, defined by the recurrence relation a n = a n − 1 + a n

number V n {\displaystyle V_{n}} can be expressed via a two-dimension recurrence relation. Closed-form expressions involve the gamma, factorial, or double

Recurrence plot, a statistical plot that shows a pattern that re-occurs Recurrence relation, an equation which defines a sequence recursively Recurrent rotation

is the case for Gaussian quadrature), the recurrence relation reduces to a three-term recurrence relation: For s < r − 1 , x p s {\displaystyle s<r-1

_{n=0}^{\infty }a_{n}x^{n}.} A recurrence relation defines each term of a sequence in terms of the preceding terms. Recurrence relations may lead to previously