In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) P n ( α , β ) ( x ) {\displaystyle P_{n}^{(\alpha ,\beta )}(x)} are...

the continuous q-Jacobi polynomials P(α,β) n(x|q), introduced by Askey & Wilson (1985), are a family of basic hypergeometric orthogonal polynomials in...

mathematics, the q-Jacobi polynomials may be the Big q-Jacobi polynomials Continuous q-Jacobi polynomials Little q-Jacobi polynomials This disambiguation...

q-Charlier polynomials q-Hahn polynomials q-Jacobi polynomials: Big q-Jacobi polynomials Continuous q-Jacobi polynomials Little q-Jacobi polynomials q-Krawtchouk...

orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The...

polynomials Little q-Jacobi polynomials Pseudo Jacobi polynomials Sieved Jacobi polynomials Jacobi preconditioner Jacobi rotation Jacobi set Jacobi sum...

mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast number of...

orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as...

The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)} and...

The Hamilton-Jacobi-Bellman (HJB) equation is a nonlinear partial differential equation that provides necessary and sufficient conditions for optimality...

1, ..., n. The modern formulation using orthogonal polynomials was developed by Carl Gustav Jacobi in 1826. The most common domain of integration for...

mathematics, the continuous Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials. They are defined...

polynomials: 4 ϕ {\displaystyle \phi } 3 Askey–Wilson | q-Racah 3 ϕ {\displaystyle \phi } 2 Continuous dual q-Hahn | Continuous q-Hahn | Big q-Jacobi...

policies. In continuous-time MDP, if the state space and action space are continuous, the optimal criterion could be found by solving Hamilton–Jacobi–Bellman...

In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication...

the elementary symmetric polynomials of the eigenvalues of A. Using Newton identities, the elementary symmetric polynomials can in turn be expressed in...

of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function...

variable, Q m = N | x m | 2 . {\displaystyle Q_{m}=N|x_{m}|^{2}.} For the case of continuous functions P ( x ) {\displaystyle P(x)} and Q ( k ) {\displaystyle...

mathematics, the Bateman polynomials are a family Fn of orthogonal polynomials introduced by Bateman (1933). The Bateman–Pasternack polynomials are a generalization...

theorem — continuous functions can be approximated uniformly by polynomials, or certain other function spaces Approximation by polynomials: Linear approximation...

U({\mathfrak {h}}_{n})} consists of real polynomials ∑ j , k → , ℓ → c j k → ℓ → z j p 1 k 1 p 2 k 2 ⋯ p n k n q 1 ℓ 1 q 2 ℓ 2 ⋯ q n ℓ n   , {\displaystyle \sum...

n = 0 ∞ q n 1 + q 2 n = − 1 4 + 1 1 − q + ( 1 − q ) 2 1 − q 3 + q ( 1 − q 2 ) 2 1 − q 5 + q 2 ( 1 − q 3 ) 2 1 − q 7 + q 3 ( 1 − q 4 ) 2 1 − q 9 + ⋯ ,...

of all such polynomials is denoted by R [ X ] {\displaystyle \mathbb {R} [X]} . Since sums and products of polynomials are again polynomials, this set R...

Hamilton–Jacobi equation (HJE) − ∂ ∂ t S ( q i , t ) = H ( q i , ∂ S ∂ q i , t ) {\displaystyle -{\frac {\partial }{\partial t}}S(q_{i},t)=H\left(q_{i},{\frac...

complete because any continuous function on [ 0 , 1 ] {\displaystyle [0,1]} can be uniformly approximated by a sequence of polynomials, by the Weierstrass...

quadratic polynomials with integer coefficients in terms of the logarithmic integral and the polynomial coefficients. No quadratic polynomial has been...

Table of spherical harmonics Vector spherical harmonics Zernike polynomials Jacobi polynomials Atomic orbital A historical account of various approaches to...

large square matrices consisting of polynomials, the Lusztig–Vogan polynomials, an analogue of Kazhdan–Lusztig polynomials introduced for reductive groups...

non-residue modulo p; it is 0 if p divides a. The same notation is used for the Jacobi symbol and Kronecker symbol, which are generalizations where p is respectively...

polynomial of order n−1. If P and Qt are nonzero polynomials in one variable, such that P(A) = 0, and if the meromorphic function f ( z ) = e t z − Q...