23 relations: Askey–Gasper inequality, Big q-Jacobi polynomials, Cambridge University Press, Carl Gustav Jacob Jacobi, Chebyshev polynomials, Classical orthogonal polynomials, Continuous q-Jacobi polynomials, Domain (mathematical analysis), Falling and rising factorials, Gamma function, Gegenbauer polynomials, Generating function, Hypergeometric function, Legendre polynomials, Linear differential equation, Little q-Jacobi polynomials, Mathematics, Orthogonal polynomials, Principal branch, Pseudo Jacobi polynomials, Rodrigues' formula, Romanovski polynomials, Zernike polynomials.
In mathematics, the Askey–Gasper inequality is an inequality for Jacobi polynomials proved by and used in the proof of the Bieberbach conjecture.
In mathematics, the big q-Jacobi polynomials Pn(x;a,b,c;q), introduced by, are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme.
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
Carl Gustav Jacob Jacobi (10 December 1804 – 18 February 1851) was a German mathematician, who made fundamental contributions to elliptic functions, dynamics, differential equations, and number theory.
In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively.
In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as a special case the Gegenbauer polynomials, Chebyshev polynomials, and Legendre polynomials).
In mathematics, the continuous q-Jacobi polynomials P(x|q), introduced by, are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme.
In mathematical analysis, a domain is any connected open subset of a finite-dimensional vector space.
In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as The rising factorial (sometimes called the Pochhammer function, Pochhammer polynomial, ascending factorial, (A reprint of the 1950 edition by Chelsea Publishing Co.) rising sequential product, or upper factorial) is defined as The value of each is taken to be 1 (an empty product) when n.
In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.
In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(x) are orthogonal polynomials on the interval with respect to the weight function (1 − x2)α–1/2.
In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.
In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases.
In mathematics, Legendre functions are solutions to Legendre's differential equation: They are named after Adrien-Marie Legendre.
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where,..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of an unknown function of the variable.
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 by.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product.
In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function.
In 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 subset of Routh polynomials it seems consistent to refer to them as Romanovski-Routh polynomials, by analogy with the terms Romanovski-Bessel and Romanovski-Jacobi used by Lesky.
In mathematics, Rodrigues' formula (formerly called the Ivory–Jacobi formula) is a formula for the Legendre polynomials independently introduced by, and.
In mathematics, Romanovski polynomials is an informal term for one of three finite subsets of real orthogonal polynomials discovered by Vsevolod Romanovsky (Romanovski in French transcription) within the context of probability distribution functions in statistics.
In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk.