Results 41 to 50 of about 324,599 (288)
Mathematics, 2023 This paper studies a new family of Angelesco multiple orthogonal polynomials with shared orthogonality conditions with respect to a system of weight functions, which are complex analogs of Pascal distributions on a legged star-like set.
Jorge Arvesú +1 more
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Discrete orthogonal polynomials on equidistant nodes [PDF]
International Mathematical Forum, 2007 In this paper we give an alternative and, in our opinion, more simple proof for the orthonormal discrete polynomials on a set of equidistant nodes. Such a proof provides a unifying explicit formulation of discrete orthonormal polynomials on an equidistant grid and an explicit formula for the coefficients of the “three-term recurrence relation”. We show
Eisinberg A, FEDELE, Giuseppe
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Casoratian Identities for the Discrete Orthogonal Polynomials in Discrete Quantum Mechanics with Real Shifts [PDF]
, 2017 In our previous papers, the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials and the Casoratian identities for the Askey-Wilson polynomial and its reduced form polynomials were presented.
S. Odake
semanticscholar +1 more source
Gottlieb Polynomials and Their q-Extensions
Mathematics, 2021 Since Gottlieb introduced and investigated the so-called Gottlieb polynomials in 1938, which are discrete orthogonal polynomials, many researchers have investigated these polynomials from diverse angles.
Esra ErkuŞ-Duman, Junesang Choi
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Extensions of discrete classical orthogonal polynomials beyond the orthogonality
Journal of Computational and Applied Mathematics, 2009 It is well known that the family of Hahn polynomials $\{h_n^{ , }(x;N)\}_{n\ge 0}$ is orthogonal with respect to a certain weight function up to $N$. In this paper we present a factorization for Hahn polynomials for a degree higher than $N$ and we prove that these polynomials can be characterized by a $ $-Sobolev orthogonality.
Costas-Santos, Roberto S. +1 more
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Uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an accumulation point [PDF]
, 2014 In this paper, we develop the Riemann–Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an accumulation point.
Xiao-Bo Wu +3 more
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Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials
Mathematics, 2020 In this paper, we consider a discrete Sobolev inner product involving the Jacobi weight with a twofold objective. On the one hand, since the orthonormal polynomials with respect to this inner product are eigenfunctions of a certain differential operator,
Juan F. Mañas-Mañas +2 more
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Mathematics, 2022 In this contribution we consider sequences of monic polynomials orthogonal with respect to the Sobolev-type inner product f,g=⟨uM,fg⟩+λTjf(α)Tjg(α), where uM is the Meixner linear operator, λ∈R+, j∈N, α≤0, and T is the forward difference operator Δ or ...
Roberto S. Costas-Santos +2 more
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Hamiltonian dynamics of a quantum of space: hidden symmetries and spectrum of the volume operator, and discrete orthogonal polynomials [PDF]
, 2013 The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given as a second ...
V. Aquilanti, D. Marinelli, A. Marzuoli
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Discrete orthogonality relations for multi-indexed Laguerre and Jacobi polynomials [PDF]
J. Math. Phys. 62, 013509 (2021), 2019 The discrete orthogonality relations hold for all the orthogonal polynomials obeying three term recurrence relations. We show that they also hold for multi-indexed Laguerre and Jacobi polynomials, which are new orthogonal polynomials obtained by deforming these classical orthogonal polynomials.
arxiv +1 more source