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...

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

dynamical systems), a linear recurrence with constant coefficients: ch. 17 : ch. 10  (also known as a linear recurrence relation or linear difference equation)...

numbers are also closely related to Lucas numbers, which obey the same recurrence relation and with the Fibonacci numbers form a complementary pair of Lucas...

as a recurrence relation: b n = n b n − 1 {\displaystyle b_{n}=nb_{n-1}} b 0 = 1 {\displaystyle b_{0}=1} This evaluation of the recurrence relation demonstrates...

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

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

G6 through a recurrence relation. Let dk = (2k + 3)k! G2k + 4, so for example, d0 = 3G4 and d1 = 5G6. Then the dk satisfy the relation ∑ k = 0 n ( n...

entries would all be 0. Stirling numbers of the second kind obey the recurrence relation { n + 1 k } = k { n k } + { n k − 1 } for 0 < k < n {\displaystyle...

{\text{Equation (2)}}} for all n≥2.{\displaystyle n\geq 2.} This is a recurrence relation giving Wn{\displaystyle W_{n}} in terms of Wn−2{\displaystyle W_{n-2}}...

0 case above but which has an extra term e−t/t. It satisfies the recurrence relation ψ ( m ) ( z + 1 ) = ψ ( m ) ( z ) + ( − 1 ) m m ! z m + 1 {\displaystyle...

\choose k}\!\!\right)=\left(\!\!{k+1 \choose n-1}\!\!\right).} A recurrence relation for multiset coefficients may be given as ( ( n k ) ) = ( ( n k −...

for the desired complexity. An alternative approach is to set up a recurrence relation for the T(n) factor, the time needed to sort a list of size n. In...

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...

the master theorem for divide-and-conquer recurrences provides an asymptotic analysis for many recurrence relations that occur in the analysis of divide-and-conquer...

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...

given expression with the determinant. The polynomials Pn satisfy a recurrence relation of the form P n ( x ) = ( A n x + B n ) P n − 1 ( x ) + C n P n −...

unsigned Stirling numbers of the first kind can be calculated by the recurrence relation [ n + 1 k ] = n [ n k ] + [ n k − 1 ] {\displaystyle \left[{n+1 \atop...

to Pascal's triangle, these numbers may be calculated using the recurrence relation pk(n)=pk−1(n−1)+pk(n−k).{\displaystyle p_{k}(n)=p_{k-1}(n-1)+p_{k}(n-k)...

Bunyakovsky conjecture. Another prime generator is defined by the recurrence relation a n = a n − 1 + gcd ( n , a n − 1 ) , a 1 = 7 , {\displaystyle a_{n}=a_{n-1}+\gcd(n...

\lfloor K/2\rfloor } , N). In aid of this, we have the following recurrence relation: p(i, j) is True if either p(i, j − 1) is True or if p(i − xj, j...

{t^{k_{0}}A_{0}\left({\frac {h}{t}}\right)-A_{0}(h)}{t^{k_{0}}-1}}.} A general recurrence relation can be defined for the approximations by A i + 1 ( h ) = t k i A...

linear recurrence relation of the form x k = n x k − 1 + x k − 2 . {\displaystyle x_{k}=nx_{k-1}+x_{k-2}.} It follows that, given such a recurrence the solution...

closest to xk-1 of the quadratic equation yk(x) = 0. This yields the recurrence relation x k = x k − 1 − 2 f ( x k − 1 ) w ± w 2 − 4 f ( x k − 1 ) f [ x k...

applies to any class of functions that can be defined by a three-term recurrence relation. In full generality, the Clenshaw algorithm computes the weighted...

_{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...

that takes one into the other. The telephone numbers satisfy the recurrence relation T ( 0 ) = 1 , {\displaystyle T(0)=1,} T ( n ) = T ( n − 1 ) + ( n...

memory. The Thue–Morse sequence is the sequence tn satisfying the recurrence relation t 0 = 0 , t 2 n = t n , t 2 n + 1 = 1 − t n , {\displaystyle...

product of the same form, for a smaller factorial. This leads to a recurrence relation, according to which each value of the factorial function can be obtained...

(1)+H_{z}.} A consequence is the following generalization of the recurrence relation: ψ ( w + 1 ) − ψ ( z + 1 ) = H w − H z . {\displaystyle \psi (w+1)-\psi...