a P-recursive equation is a linear equation of sequences where the coefficient sequences can be represented as polynomials. P-recursive equations are...

In mathematics a P-recursive equation can be solved for polynomial solutions. Sergei A. Abramov in 1989 and Marko Petkovšek in 1992 described an algorithm...

solutions of linear difference equations with polynomial coefficients are called P-recursive. For these specific recurrence equations algorithms are known which...

A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known...

{\displaystyle s_{0},s_{1},s_{2},s_{3},\ldots } is called constant-recursive if it satisfies an equation of the form s n = c 1 s n − 1 + c 2 s n − 2 + ⋯ + c d s...

Bethe–Salpeter equation appears in many forms. One form often used in high energy physics is Γ ( P , p ) = ∫ d 4 k ( 2 π ) 4 K ( P , p , k ) S ( k − P 2 ) Γ ( P ,...

10  (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of...

primitive recursive function terminology": In the definition of ρ ( g , h ) {\displaystyle \rho (g,h)} , the first equation suggests to choose g = P 1 1 {\displaystyle...

is sometimes represented in what is called an Euler equation. A time-series path in the recursive model is the result of a series of these two-period...

Lane-Emden equation, we can show that all odd coefficients of the series vanish a 2 m + 1 = 0 {\displaystyle a_{2m+1}=0} . Furthermore, we obtain a recursive relationship...

Recursive least squares (RLS) is an adaptive filter algorithm that recursively finds the coefficients that minimize a weighted linear least squares cost...

called holonomic. Holonomic sequences are also called P-recursive sequences: they are defined recursively by multivariate recurrences satisfied by the whole...

 2, 1 can be found by working backwards, using a recursive relationship called the Bellman equation. For i = 2, ..., n, Vi−1 at any state y is calculated...

solutions to smaller instances of the same problem. Recursion solves such recursive problems by using functions that call themselves from within their own...

Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form x 2 − n y 2 = 1 , {\displaystyle x^{2}-ny^{2}=1,} where...

corresponding equation. The unsolvability of Hilbert's tenth problem is a consequence of the surprising fact that the converse is true: Every recursively enumerable...

all such languages in P are expressible in first-order logic with the addition of a suitable least fixed-point combinator. Recursive functions can be defined...

are equations which define one or more sequences recursively. Some specific kinds of recurrence relation can be "solved" to obtain a non-recursive definition...

{\displaystyle S(0)=0} is a negated proposition. Further, recursive defining equations for every primitive recursive function may be adopted as axioms as desired....

Pergamon Press 1963, Dover 2007 Recursive number theory - a development of recursive arithmetic in a logic-free equation calculus, North Holland 1957 Constructive...

In mathematics, the Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow...

{-c}{x}}\\x&=-b-{\frac {c}{x}}\,\end{aligned}}} But now we can apply the last equation to itself recursively to obtain x = − b − c − b − c − b − c − b − c − b − ⋱ {\displaystyle...

by a combination of relaxation and appeal to still coarser grids. This recursive process is repeated until a grid is reached where the cost of direct solution...

fidelity, ray tracing-based rendering techniques, such as ray casting, recursive ray tracing, distribution ray tracing, photon mapping and path tracing...

Structural induction is used to prove that some proposition P(x) holds for all x of some sort of recursively defined structure, such as formulas, lists, or trees...

in functional programming languages, and provide a means to allow for recursive definitions. In the classical untyped lambda calculus, every function...

ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is...

uncountable ordinal, ω1), described below. Ordinal numbers below ωCK 1 are the recursive ordinals (see below). Countable ordinals larger than this may still be...

Consider a problem that can be solved using a recursive algorithm such as the following: procedure p(input x of size n): if n < some constant k: Solve...

on the Fresnel equations, but with additional calculations to account for interference. The transfer-matrix method, or the recursive Rouard method  can...