Results 51 to 60 of about 972,343 (359)

Mehler-Heine asymptotics for multiple orthogonal polynomials

, 2016
Mehler-Heine asymptotics describe the behavior of orthogonal polynomials near the edges of the interval where the orthogonality measure is supported. For Jacobi polynomials and Laguerre polynomials this asymptotic behavior near the hard edge involves ...
Van Assche, Walter
core   +1 more source

Vibration of beams using novel boundary characteristic orthogonal polynomials satisfying all boundary conditions

Advances in Mechanical Engineering, 2015
Boundary characteristic orthogonal polynomials proposed by the author in 1985 have been used in the Rayleigh Ritz method extensively in order to obtain natural frequencies of vibrating plates with different boundary conditions.
Rama B Bhat
doaj   +1 more source

Nearest Neighbor Recurrence Relations for Meixner–Angelesco Multiple Orthogonal Polynomials of the Second Kind

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, Alejandro J. Quintero Roba   +1 more
doaj   +1 more source

Singular Values of Products of Ginibre Random Matrices, Multiple Orthogonal Polynomials and Hard Edge Scaling Limits [PDF]

, 2013
Akemann, Ipsen and Kieburg recently showed that the squared singular values of products of M rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a correlation kernel that ...
A. Kuijlaars, Lun Zhang
semanticscholar   +1 more source

Block orthogonal polynomials: I. Definition and properties

, 2007
Constrained orthogonal polynomials have been recently introduced in the study of the Hohenberg-Kohn functional to provide basis functions satisfying particle number conservation for an expansion of the particle density.
Abramowitz M, Andrews G E, Bateman H, Bourbaki N, Chihara T S, Dieudonné J, Dreizler R M, Fiolhais C, Giraud B G, Gradshteyn I S, Halmos P R, Jean-Marie Normand, Kreyszig E, Lang S, Mehta M L, Messiah A, Normand J-M, Szegö G   +17 more
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Some Orthogonal Polynomials Arising from Coherent States [PDF]

, 2011
We explore in this paper some orthogonal polynomials which are naturally associated to certain families of coherent states, often referred to as nonlinear coherent states in the quantum optics literature.
Akhiezer N I, Andrews G E, Askey R, Chihara T S, Dickinson D J, Erdélyi A, Feller W, Goldberg J, Ismail M E H, Ismail M E H, Klauder J R, Koekoek R Swarttouw R, Mourad E H Ismail, Nevai P, Odzijewicz A, Rainville E D, S Twareque Ali, Sivakumar S, Szegő G, Widder D V   +19 more
core   +1 more source

On Certain Properties and Applications of the Perturbed Meixner–Pollaczek Weight

Mathematics, 2021
This paper deals with monic orthogonal polynomials orthogonal with a perturbation of classical Meixner–Pollaczek measure. These polynomials, called Perturbed Meixner–Pollaczek polynomials, are described by their weight function emanating from an ...
Abey S. Kelil, Alta S. Jooste, Appanah R. Appadu   +2 more
doaj   +1 more source

Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials

Advances in Mathematical Physics, 2018
Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived.
Oksana Bihun, Clark Mourning
doaj   +1 more source

Explicit barycentric weights for polynomial interpolation in the roots or extrema of classical orthogonal polynomials [PDF]

Mathematics of Computation, 2012
Barycentric interpolation is arguably the method of choice for numerical polynomial interpolation. In this paper we show that barycentric weights for the roots or extrema of classical families of orthogonal polynomials are expressible explicitly in terms
Haiyong Wang, D. Huybrechs, S. Vandewalle   +2 more
semanticscholar   +1 more source

Asymptotics of skew orthogonal polynomials

, 2000
Exact integral expressions of the skew orthogonal polynomials involved in Orthogonal (beta=1) and Symplectic (beta=4) random matrix ensembles are obtained: the (even rank) skew orthogonal polynomials are average characteristic polynomials of random ...
B Eynard, Bonnet G, Brezin E, Christoffel E, Darboux G, Deift P, Eynard B, Heine E, Kunz H, Mehta M, Mehta M L, Pastur L, Szego G, Tracy C A   +13 more
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