Results 81 to 90 of about 122,453 (243)
Differential equations for generalized Jacobi polynomials [PDF]
Journal of Computational and Applied Mathematics, 2000 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 two point masses at the endpoints of the interval of orthogonality.
Koekoek, J. (author) +1 more
openaire +5 more sources
A new family of orthogonal polynomials in three variables
Journal of Inequalities and Applications, 2020 In this paper we introduce a six-parameter generalization of the four-parameter three-variable polynomials on the simplex and we investigate the properties of these polynomials.
Rabia Aktaş +2 more
doaj +1 more source
Multi-variable orthogonal polynomials [PDF]
arXiv, 2014 We characterize the atomic probability measure on $\mathbb{R}^d$ which having a finite number of atoms. We further prove that the Jacobi sequences associated to the multiple Hermite (resp. Laguerre, resp. Jacobi) orthogonal polynomials are diagonal matrices.
arxiv
A transference result of the $L^p$ continuity of the Jacobi Riesz transform to the Gaussian and Laguerre Riesz transforms [PDF]
, 2012 In this paper using the well known asymptotic relations between Jacobi polynomials and Hermite and Laguerre polynomials. We develop a transference method to obtain the $L^p$-continuity of the Gaussian-Riesz transform and the $L^p$-continuity of the ...
Eduard Navas, O. Urbina, Wilfredo
core
On Jacobi and continuous Hahn polynomials [PDF]
arXiv, 1994 Jacobi polynomials are mapped onto the continuous Hahn polynomials by the Fourier transform and the orthogonality relations for the continuous Hahn polynomials then follow from the orthogonality relations for the Jacobi polynomials and the Parseval formula.
arxiv
, 2006 For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q=0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations.
A. Okounkov +16 more
core +2 more sources
On the Extreme Zeros of Jacobi Polynomials
, 2023 By applying the Euler--Rayleigh methods to a specific representation of the Jacobi polynomials as hypergeometric functions, we obtain new bounds for their largest zeros. In particular, we derive upper and lower bound for $1-x_{nn}^2( )$, with $x_{nn}( )$ being the largest zero of the $n$-th ultraspherical polynomial $P_n^{( )}$.
openaire +2 more sources
Advances in Difference Equations, 2019 In this paper, we investigate sums of finite products of Chebyshev polynomials of the first kind and those of Lucas polynomials. We express each of them as linear combinations of Hermite, extended Laguerre, Legendre, Gegenbauer, and Jacobi polynomials ...
Taekyun Kim +3 more
doaj +1 more source
Alternative Jacobi Polynomials and Orthogonal Exponentials [PDF]
arXiv, 2011 Sequences of orthogonal polynomials that are alternative to the Jacobi polynomials on the interval $[0,1]$ are defined and their properties are established. An $(\alpha,\beta)$-parameterized system of orthogonal polynomials of the exponential function on the semi-axis $[0,\infty)$ is presented.
arxiv
Cohomological relation between Jacobi forms and skew-holomorphic Jacobi forms [PDF]
arXiv, 2013 Eichler and Zagier developed a theory of Jacobi forms to understand and extend Maass' work on the Saito-Kurokawa conjecture. Later Skoruppa introduced skew-holomorphic Jacobi forms, which play an important role in understanding liftings of modular forms and Jacobi forms.
arxiv