combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients: ch. 17 : ch. 10 (also known as a linear recurrence relation...
25 KB (4,667 words) - 20:58, 16 May 2024
the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the...
25 KB (4,165 words) - 12:55, 14 August 2024
true for a linear equation of order one, with non-constant coefficients. An equation of order two or higher with non-constant coefficients cannot, in...
30 KB (4,757 words) - 05:05, 8 August 2024
Characteristic equation (calculus) (category Articles with short description)
r^{n}-b_{1}r^{n-1}-\cdots -b_{n}=0,} discussed in more detail at Linear recurrence with constant coefficients. The characteristic roots (roots of the characteristic...
13 KB (1,989 words) - 16:10, 14 August 2024
numbers, or complex numbers). The equation is called a linear recurrence with constant coefficients of order d. The order of the sequence is the smallest...
37 KB (5,025 words) - 09:51, 17 July 2024
Fibonacci sequence (redirect from Tetranacci constant)
Édouard Lucas. Like every sequence defined by a homogenous linear recurrence with constant coefficients, the Fibonacci numbers have a closed-form expression...
86 KB (12,984 words) - 10:04, 21 August 2024
Sequence (category Articles with short description)
{\text{otherwise}},\end{cases}}} with initial term a 0 = 0. {\displaystyle a_{0}=0.} A linear recurrence with constant coefficients is a recurrence relation of the form...
39 KB (6,156 words) - 04:01, 4 August 2024
Skolem problem (category Recurrence relations)
sequence satisfying a linear recurrence with constant coefficients. This theorem states that, if such a sequence has zeros, then with finitely many exceptions...
5 KB (572 words) - 20:18, 18 January 2023
the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by...
61 KB (10,577 words) - 15:58, 14 August 2024
Generating function (category Articles with short description)
of polynomials satisfies a linear recurrence with constant coefficients; these coefficients are identical to the coefficients of the fraction denominator...
87 KB (14,536 words) - 21:20, 20 August 2024
Partial differential equation (redirect from Linear partial differential equation)
the discussion of linearity.) If the ai are constants (independent of x and y) then the PDE is called linear with constant coefficients. If f is zero everywhere...
49 KB (6,849 words) - 16:29, 8 July 2024
Frobenius method (category Articles with short description)
zero), the coefficients of all series involved in second linearly independent solutions can be calculated straightforwardly from tandem recurrence relations...
13 KB (2,955 words) - 16:05, 30 May 2024
Ordinary differential equation (redirect from Linear ordinary differential equations)
Method of undetermined coefficients Recurrence relation Dennis G. Zill (15 March 2012). A First Course in Differential Equations with Modeling Applications...
44 KB (4,890 words) - 14:21, 20 August 2024
Tausworthe, Robert C. (April 1965). "Random Numbers Generated by Linear Recurrence Modulo Two" (PDF). Mathematics of Computation. 19 (90): 201–209. doi:10...
37 KB (4,672 words) - 10:41, 22 June 2024
Clenshaw algorithm (redirect from Clenshaw recurrence)
_{k},\;k=0,1,\ldots } is a sequence of functions that satisfy the linear recurrence relation ϕ k + 1 ( x ) = α k ( x ) ϕ k ( x ) + β k ( x ) ϕ k − 1 (...
10 KB (2,169 words) - 13:05, 19 August 2024
Rational function (category Articles with short description)
satisfies a linear recurrence determines a rational function when used as the coefficients of a Taylor series. This is useful in solving such recurrences, since...
16 KB (2,355 words) - 15:52, 3 June 2024
Mersenne Twister (category Articles with short description)
[0,2^{w}-1]} . The Mersenne Twister algorithm is based on a matrix linear recurrence over a finite binary field F 2 {\displaystyle {\textbf {F}}_{2}} ...
32 KB (4,014 words) - 16:27, 19 August 2024
undetermined coefficients is an approach to finding a particular solution to certain nonhomogeneous ordinary differential equations and recurrence relations...
10 KB (1,812 words) - 07:52, 23 October 2022
applied to this differential equation with step size h yields a linear recurrence relation with characteristic polynomial π ( z ; h λ ) = ( 1 − h λ β s ) z...
23 KB (4,865 words) - 02:04, 1 November 2023
Equation (category Articles with short description)
other terms, which are assumed to be known, are usually called constants, coefficients or parameters. An example of an equation involving x and y as unknowns...
32 KB (4,237 words) - 20:34, 10 August 2024
Holonomic function (category Articles with short description)
satisfies a linear homogeneous recurrence relation with polynomial coefficients, or equivalently a linear homogeneous difference equation with polynomial...
13 KB (1,977 words) - 15:36, 18 August 2024
Multiset (redirect from Multiset coefficient)
coefficients, there is a negative binomial distribution in which the multiset coefficients occur. Multiset coefficients should not be confused with the...
35 KB (4,850 words) - 15:37, 3 August 2024
Differential equation (category Articles with short description)
constant coefficient ordinary differential equation: d u d x = c u + x 2 . {\displaystyle {\frac {du}{dx}}=cu+x^{2}.} Homogeneous second-order linear...
29 KB (3,628 words) - 15:16, 20 August 2024
Companion matrix (category Articles with short description)
for some purposes such as linear recurrence relations (see below). C ( p ) {\displaystyle C(p)} is defined from the coefficients of p ( x ) {\displaystyle...
11 KB (2,443 words) - 12:08, 25 June 2024
Symbolic integration (category Articles with short description)
the coefficients of their Taylor series at any point satisfy a linear recurrence relation with polynomial coefficients, and that this recurrence relation...
9 KB (1,198 words) - 14:22, 24 January 2024
P-recursive equation (category Articles with short description)
linear recurrence equations (or linear recurrence relations or linear difference equations) with polynomial coefficients. These equations play an important...
14 KB (2,216 words) - 01:05, 3 December 2023
Wave equation (redirect from Linear wave equation)
Bott, L. Garding, "Lacunas for hyperbolic differential operators with constant coefficients I", Acta Mathematica, 124 (1970), 109–189. M. F. Atiyah, R. Bott...
69 KB (12,069 words) - 12:23, 23 August 2024
Lucas sequence (category Recurrence relations)
Q ) {\displaystyle V_{n}(P,Q)} are certain constant-recursive integer sequences that satisfy the recurrence relation x n = P ⋅ x n − 1 − Q ⋅ x n − 2 {\displaystyle...
21 KB (3,958 words) - 23:51, 10 May 2024
Transcendental number (category Articles with short description)
that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients. The best-known transcendental numbers are π and...
51 KB (6,761 words) - 13:32, 23 August 2024
Z-transform (category Articles with short description)
provided a systematic and effective method for solving linear difference equations with constant coefficients, which are ubiquitous in the analysis of discrete-time...
38 KB (4,621 words) - 11:36, 3 June 2024