Results 1 to 10 of about 122,453 (243)
Upward extension of the Jacobi matrix for orthogonal polynomials [PDF]
arXiv, 1995 Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We investigate new orthogonal polynomials by adding to the Jacobi matrix $r$ new rows and columns, so that the original
A. Ronveaux, Walter Van Assche
arxiv +7 more sources
On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials.
Tom H. Koornwinder
doaj +24 more sources
Jacobi’s generating function for Jacobi polynomials [PDF]
Proceedings of the American Mathematical Society, 1978 An idea of Hermite is used to give a simple proof of Jacobi’s generating function for Jacobi polynomials.
Richard Askey
openalex +3 more sources
Representation of ( p , q ) $(p,q)$ -Bernstein polynomials in terms of ( p , q ) $(p,q)$ -Jacobi polynomials [PDF]
Journal of Inequalities and Applications, 2017 A representation of ( p , q ) $(p,q)$ -Bernstein polynomials in terms of ( p , q ) $(p,q)$ -Jacobi polynomials is obtained.
F Soleyman +3 more
doaj +2 more sources
An algebraic treatment of the Askey biorthogonal polynomials on the unit circle [PDF]
Forum of Mathematics, Sigma, 2021 A joint algebraic interpretation of the biorthogonal Askey polynomials on the unit circle and of the orthogonal Jacobi polynomials is offered. It ties their bispectral properties to an algebra called the meta-Jacobi algebra $m\mathfrak {J}$ .
Luc Vinet, Alexei Zhedanov
doaj +2 more sources
Properties of the Polynomials Associated with the Jacobi Polynomials [PDF]
Mathematics of Computation, 1986 Power forms and Jacobi polynomial forms are found for the polynomials W n ( α , β ) W_n^{(\alpha ,\beta )} associated with Jacobi polynomials. Also, some differential-difference equations and evaluations of certain integrals involving W n
Stanis Law Lewanowicz
openalex +3 more sources
Jacobi Polynomials as Generalized Faber Polynomials [PDF]
Transactions of the American Mathematical Society, 1990 Let B {\mathbf {B}} be an open bounded subset of the complex z z -plane with closure B ¯ \overline {\mathbf {B}} whose complement B ¯ c {
Ahmed I. Zayed
openalex +3 more sources
The Jacobi inversion formula [PDF]
Complex Variables 39 (1999) 1-18, 1999 We look for spectral type differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with point masses at the endpoints of the interval of orthogonality.
Koekoek, J., Koekoek, R.
arxiv +4 more sources
New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems [PDF]
The Scientific World Journal, 2014 This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials ...
W. M. Abd-Elhameed
doaj +2 more sources
Multiple Wilson and Jacobi-Pineiro polynomials [PDF]
J. Approx. Theory 132 (2005), 155-181, 2003 We introduce multiple Wilson polynomials, which give a new example of multiple orthogonal polynomials (Hermite-Pade polynomials) of type II. These polynomials can be written as a Jacobi-Pineiro transform, which is a generalization of the Jacobi transform for Wilson polynomials, found by T.H. Koornwinder.
Bernhard Beckermann +2 more
arxiv +3 more sources