Results 41 to 50 of about 126,262 (211)
Sylvester equations for Laguerre–Hahn orthogonal polynomials on the real line [PDF]
, 2013 Matrix Sylvester differential equations are introduced in the study of Laguerre–Hahn orthogonal polynomials. Matrix Sylvester differential systems are shown to yield representations for the Laguerre–Hahn orthogonal polynomials.
Branquinho, A. +4 more
core +1 more source
Beating the Standard Quantum Limit With Single‐Photon‐Added Coherent States
Advanced Physics Research, Volume 5, Issue 10, October 2026.The standard quantum limit (SQL) defines how quantum fluctuations of light constrain measurement precision. Here, we show that injecting a single‐photon‐added coherent state and a weak coherent state in the input ports of a Mach–Zehnder interferometer reduces phase uncertainty below the SQL.
Pankaj K. Jha +4 more
wiley +1 more source
Comparison between the Propagation Properties of Bessel–Gauss and Generalized Laguerre–Gauss Beams
Photonics, 2023 The connections between Laguerre–Gauss and Bessel–Gauss beams, and between Hermite–Gauss and cosine-Gauss beams are investigated. We review different asymptotic expressions for generalized Laguerre and Hermite polynomials of large radial/transverse order.
Colin J. R. Sheppard, Miguel A. Porras
doaj +1 more source
On multiple q-Laguerre polynomials
Journal of Classical Analysis, 2023 Summary: We study \(q\)-Laguerre multiple orthogonal polynomials. These polynomials are orthogonal with respect to \(q\)-analogues of Laguerre weight functions. We focus our attention on their structural properties. Raising and lowering operators as well as Rodrigues-type formulas are obtained and their explicit representations are given.
Sadjang, P. Njionou +2 more
openaire +2 more sources
International Journal for Numerical Methods in Fluids, Volume 98, Issue 10, Page 1143-1164, October 2026.This article provides important geometric formulas for node‐centered, edge‐based schemes in any number of dimensions. These formulas are noteworthy, as they do not require the explicit formation of dual regions. We prove several key geometric results, with a particular focus on the four‐dimensional case, due to potential space‐time applications ...
Nicholas Tufillaro +2 more
wiley +1 more source
Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems
Abstract and Applied Analysis, 2013 We present a direct solution technique for approximating linear multiterm fractional differential equations (FDEs) on semi-infinite interval, using generalized Laguerre polynomials.
D. Baleanu, A. H. Bhrawy, T. M. Taha
doaj +1 more source
Communications on Pure and Applied Mathematics, Volume 79, Issue 9, Page 2107-2157, September 2026.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
wiley +1 more source
Catalan polynomials for the Wishart-Laguerre
Physics Letters BBy means of W -representation, we investigate the Wishart-Laguerre β -ensemble and present a compact expression for Catalan polynomials. For a special Nekrasov partition function associated with the Wishart-Laguerre β -ensemble, we show that it can be ...
Bei Kang +3 more
doaj +1 more source
Spatial signatures of group cohesion
Methods in Ecology and Evolution, Volume 17, Issue 9, Page 2755-2769, September 2026.Abstract Wildlife populations are undergoing unprecedented changes to their spatial distributions as a result of human activities. Innovative approaches are needed to document these changes, especially in cases where sampling is sparse. Here, we contribute to the tools available in spatial ecology by developing novel metrics based on the coefficient of
Nicola E. Love, Sarah P. Otto
wiley +1 more source
Edge Density Expansions for the Classical Gaussian and Laguerre Ensembles
Studies in Applied Mathematics, Volume 157, Issue 3, September 2026.ABSTRACT Recent work of Bornemann has uncovered hitherto hidden integrable structures relating to the asymptotic expansion of quantities at the soft edge of the Gaussian and Laguerre random matrix ensembles. These quantities are spacing distributions and the eigenvalue density, and the findings cover the cases of the three symmetry classes: orthogonal,
Peter J. Forrester +2 more
wiley +1 more source