combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients: ch. 17 : ch. 10  (also known as a linear recurrence relation...

the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the...

Lucas. Like every sequence defined by a homogeneous linear recurrence with constant coefficients, the Fibonacci numbers have a closed-form expression...

the differential equation is linear and homogeneous, and has constant coefficients. Such a differential equation, with y as the dependent variable, superscript...

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...

sequence satisfying a linear recurrence with constant coefficients. This theorem states that, if such a sequence has zeros, then with finitely many exceptions...

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

{y_{n+1}-y_{n}}{h}}=-\kappa y_{n},} which implies the first-order linear recurrence with constant coefficients y n + 1 = y n ( 1 − h κ ) . {\displaystyle y_{n+1}=y_{n}(1-h\kappa...

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...

{\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...

the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by...

of polynomials satisfies a linear recurrence with constant coefficients; these coefficients are identical to the coefficients of the fraction denominator...

undetermined coefficients is an approach to finding a particular solution to certain nonhomogeneous ordinary differential equations and recurrence relations...

{\displaystyle \{b_{n}\}} are constant and independent of the step index n, then the TTRR is a Linear recurrence with constant coefficients of order 2. Arguably...

solutions to a special class of linear difference equation: inhomogeneous first order linear recurrences with constant coefficients. The elements of an arithmetico-geometric...

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...

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...

satisfies a linear homogeneous recurrence relation with polynomial coefficients, or equivalently a linear homogeneous difference equation with polynomial...

constant coefficient ordinary differential equation: d u d x = c u + x 2 . {\displaystyle {\frac {du}{dx}}=cu+x^{2}.} Homogeneous second-order linear...

zero), the coefficients of all series involved in second linearly independent solutions can be calculated straightforwardly from tandem recurrence relations...

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...

{\displaystyle s(x)} such that the coefficients of the k {\displaystyle k} largest monomials are equal to the corresponding coefficients of p ( x ) {\displaystyle...

[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}} ...

one wishes to have recurrence relations for r̃i = Qi(A)Pi(A)r0 where Qi(A) = (I − ω1A)(I − ω2A)⋯(I − ωiA) with suitable constants ωj instead of ri = Pi(A)r0...

_{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 (...

Tausworthe, Robert C. (April 1965). "Random Numbers Generated by Linear Recurrence Modulo Two" (PDF). Mathematics of Computation. 19 (90): 201–209. doi:10...

linear recurrence equations (or linear recurrence relations or linear difference equations) with polynomial coefficients. These equations play an important...

the linear recurrence relation F ( i ) = F ( i − 2 ) + F ( i − 4 ) {\displaystyle F(i)=F(i-2)+F(i-4)} (a modified form of the Fibonacci recurrence), starting...

sequence defined by a linear recurrence whose coefficients are those of the polynomial. Since the method converges with a linear order only, it is less...

the coefficients of their Taylor series at any point satisfy a linear recurrence relation with polynomial coefficients, and that this recurrence relation...