Results 51 to 60 of about 19,826 (260)
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
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Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract The representation of an analytic function as a series involving q$q$‐polynomials is a fundamental problem in classical analysis and approximation theory [Ramanujan J. 19 (2009), no. 3, 281–303]. In this paper, our investigation is focusing on q$q$‐analog complex Hermite polynomials, which were motivated by Ismail and Zhang [Adv. Appl.
Jian Cao
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
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, 2010 Simple derivation is presented of the four families of infinitely many shape invariant Hamiltonians corresponding to the exceptional Laguerre and Jacobi polynomials.
Agarwal R P +19 more
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A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland type [PDF]
, 2009 In this paper we consider a large class of many-variable polynomials which contains generalisations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cases, and which occur as the polynomial part in the eigenfunctions of ...
Hallnäs, Martin, Langmann, Edwin
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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
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Automated measurement of detectability index in CT imaging: Development and validation
Journal of Applied Clinical Medical Physics, Volume 26, Issue 11, November 2025.Abstract Purpose The purpose of this study is to develop software for measuring the detectability index (d′) automatically from ACR 464 CT phantom images. Method Software for measuring d′ automatically was developed with Python 3.9.13 using the PyQt5 graphical user interface (GUI) as part of the IndoQCT platform.
Choirul Anam +7 more
wiley +1 more source
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
, 2005 The equilibrium positions of the multi-particle classical Calogero-Sutherland-Moser (CSM) systems with rational/trigonometric potentials associated with the classical root systems are described by the classical orthogonal polynomials; the Hermite ...
Odake, S., Sasaki, R.
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Connection coefficients for Laguerre-Sobolev orthogonal polynomials [PDF]
, 2003 19 pages, no figures.-- MSC2000 codes: 33C45, 42C05.MR#: MR1991819 (2004h:33020)Zbl#: Zbl 1033.42027^aLaguerre–Sobolev polynomials are orthogonal with respect to an inner product of the form $$\langle p,q\rangle=\int_0^{\infty}p(x)q(x)x^{\alpha}e^{-x ...
Marcellán Español, Francisco José +1 more
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