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

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

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

of the first to introduce and study the symmetric polynomials that are now known as Schur polynomials, giving the so-called bialternant formula for these...

mathematics, the term Pseudo Jacobi polynomials was introduced by Lesky for one of three finite sequences of orthogonal polynomials y. Since they form an orthogonal...

(1 − x2)α–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials. They are named after Leopold Gegenbauer...

In mathematics, sieved Jacobi polynomials are a family of sieved orthogonal polynomials, introduced by Askey (1984). Their recurrence relations are a modified...

that space a basis of orthogonal polynomials, the Bergman polynomials. In this case, the analog of the tridiagonal Jacobi operator is a Hessenberg operator...

manifolds Jacobi operator (Jacobi matrix), a tridiagonal symmetric matrix appearing in the theory of orthogonal polynomials Jacobi polynomials, a class...

In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike...

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

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

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

turns Jacobi polynomials into Gegenbauer polynomials, in which case the technique is sometimes called Gauss–Gegenbauer quadrature. Gauss–Jacobi quadrature...

big q-Jacobi polynomials Pn(x;a,b,c;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. The polynomials are given...

Laguerre polynomials Chebyshev polynomials Legendre polynomials Jacobi polynomials Others come from statistics: Hermite polynomials Many are studied in algebra...

elementary symmetric polynomials and the complete homogeneous symmetric polynomials. In representation theory they are the characters of polynomial irreducible...

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

In mathematics, the little q-Jacobi polynomials pn(x;a,b;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced...

to define the multidimensional polynomials. Like the other classical orthogonal polynomials, the Hermite polynomials can be defined from several different...

Jacobi matrix may refer to: Jacobian matrix and determinant of a smooth map between Euclidean spaces or smooth manifolds Jacobi operator (Jacobi matrix)...

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

Romanovski–Jacobi used by Lesky for two other sets of orthogonal polynomials. In some contrast to the standard classical orthogonal polynomials, the polynomials...

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

G. (1943). "On the oscillations of differential transforms. IV. Jacobi polynomials". Trans. Amer. Math. Soc. 53 (3): 463–468. doi:10.1090/s0002-9947-1943-0008100-4...

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

orthogonal polynomials of ( q {\displaystyle q} -)hypergeometric type into a hierarchy. The Askey–Gasper inequality for Jacobi polynomials is essential...

mathematics, Jacobi transform is an integral transform named after the mathematician Carl Gustav Jacob Jacobi, which uses Jacobi polynomials P n α , β (...

polynomials Heat polynomial — see caloric polynomial Heckman–Opdam polynomials Hermite polynomials Hurwitz polynomial Jack function Jacobi polynomials Koornwinder...

The Jacobi symbol is a generalization of the Legendre symbol. Introduced by Jacobi in 1837, it is of theoretical interest in modular arithmetic and other...