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

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...

q){z^{k}}.\end{aligned}}} The Kravchuk polynomials satisfy the three-term recurrence relation x K k ( x ; n , q ) = − q ( n − k ) K k + 1 ( x ; n , q ) +...

states that a sequence of polynomials satisfying a suitable three-term recurrence relation is a sequence of orthogonal polynomials. The theorem was introduced...

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...

a three-term recurrence relation. It can be shown that there is no Krylov subspace method for general matrices, which is given by a short recurrence relation...

called continuants, of the nth convergent. They are given by the three-term recurrence relation A n = b n A n − 1 + a n A n − 2 , B n = b n B n − 1 + a n B...

kind. As discussed above, the Legendre polynomials obey the three-term recurrence relation known as Bonnet's recursion formula given by ( n + 1 ) P n +...

of a tridiagonal matrix A of order n can be computed from a three-term recurrence relation. Write f1 = |a1| = a1 (i.e., f1 is the determinant of the 1...

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

R_{m+2}^{m}(\rho )=((m+2)\rho ^{2}-(m+1))\rho ^{m}} . The following three-term recurrence relation then allows to calculate all other R n m ( ρ ) {\displaystyle...

Miller's recurrence algorithm is a procedure for the backward calculation of a rapidly decreasing solution of a three-term recurrence relation developed...

their method for computing Gaussian quadrature rules given the three term recurrence relation that the underlying orthogonal polynomials satisfy. They reduce...

why sequences of orthogonal polynomials can always be given a three-term recurrence relation.) For k = j − 1 {\displaystyle k=j-1} one gets h j − 1 , j =...

representation of the generalized Marcum Q-function. The related three-term recurrence relation is given by Q ν + 1 ( a , b ) − ( 1 + c ν ( a , b ) ) Q ν (...

the recurrence as a matrix eigenvalue problem, or implementing a backwards recurrence algorithm. The complexity of the three-term recurrence relation is...

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...

(2021-08-01). "Asymptotic Behaviour of Christoffel–Darboux Kernel Via Three-Term Recurrence Relation I". Constructive Approximation. 54 (1): 49–116. arXiv:1909.09107...

order, homogeneous linear recurrence with constant coefficients. Geometric sequences also satisfy the nonlinear recurrence relation a n = a n − 1 2 / a n...

operator. It also arises in: The Lax pair of the Toda lattice. The three-term recurrence relationship of orthogonal polynomials, orthogonal over a positive...

( 1 ) = P ( 2 ) = 1 , {\displaystyle P(0)=P(1)=P(2)=1,} and the recurrence relation P ( n ) = P ( n − 2 ) + P ( n − 3 ) . {\displaystyle P(n)=P(n-2)+P(n-3)...

_{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...

constants. The equation is called a linear recurrence relation. The concept is also known as a linear recurrence sequence, linear-recursive sequence, linear-recurrent...

f_{2},\dots } be a sequence of analytic functions that obey the three-term recurrence relation f i − 1 = f i + k i z f i + 1 {\displaystyle f_{i-1}=f_{i}+k_{i}\...

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...

{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...

method proceeds according to a third-order recurrence relation similar to the second-order recurrence relation of the secant method. Whereas the secant...

proof We prove the recurrence relation using the definition of Stirling numbers in terms of rising factorials. Distributing the last term of the product,...

{\displaystyle n\geq 1} . This gives a recurrence relation defining p(n) in terms of an, and vice versa a recurrence for an in terms of p(n). Thus, our desired...

that the will to power must be considered in relation to the Übermensch and the thought of eternal recurrence—although this reading itself has been criticized...