Results 11 to 20 of about 2,012 (183)
Irreducibility of extensions of Laguerre polynomials [PDF]
Functiones et Approximatio Commentarii Mathematici, 2020 For integers $a_0,a_1,\ldots,a_n$ with $|a_0a_n|=1$ and either $ =u$ with $1\leq u \leq 50$ or $ =u+ \frac{1}{2}$ with $1 \leq u \leq 45$, we prove that $ _n^{( )}(x;a_0,a_1,\cdots,a_n)$ is irreducible except for an explicit finite set of pairs $(u,n)$. Furthermore all the exceptions other than $n=2^{12}, =89/2$ are necessary.
Laishram, Shanta +2 more
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Specializations of Generalized Laguerre Polynomials [PDF]
SIAM Journal on Mathematical Analysis, 1994 Three specializations of a set of orthogonal polynomials with ``8 different q's'' are given. The polynomials are identified as $q$-analogues of Laguerre polynomials, and the combinatorial interpretation of the moments give infinitely many new Mahonian statistics on permutations.
Dennis Stanton, Rodica Simion
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On Appell-Laguerre polynomials
Journal of Computational and Applied Mathematics, 1993 The author considers so-called Appell-Laguerre polynomials, given explicitly by \[ Q_ n(x;k)=c_ n \sum_{j=0}^ n{(-n)_ j x^ j\over (\alpha+k+1-n)_ j j!} \quad (k,n \in {\mathcal N}). \] He gives a generating function and facts about the simplicity and location of the zeros; for the proofs the author refers to his paper Rodrigues' formula revisited ...
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Laguerre polynomials as Jensen polynomials of Laguerre–Pólya entire functions
Journal of Computational and Applied Mathematics, 2009 AbstractWe prove that the only Jensen polynomials associated with an entire function in the Laguerre–Pólya class that are orthogonal are the Laguerre polynomials.
Dimitrov, Dimitar Kolev +1 more
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Generalizations of Laguerre polynomials
Journal of Mathematical Analysis and Applications, 1990 The main aim of the author is to show that the constants \(A_ 0,A_ 1,\dots,A_{N+1}\) can appropriately be chosen such that the polynomials \[ L_ n^{\alpha,M_ 0,M_ 1,\dots,M_ n}(x)=\sum_{k=0}^{N+1} A_ k D^ k L_ n^{(\alpha)}(x); \qquad \alpha>-1; \quad n=0,1,\dots \leqno(*) \] constitute an orthogonal set with respect to the following inner product ...
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Matrix Valued Laguerre Polynomials [PDF]
, 2019 20 pages, to appear in Positivity and Noncommutative Analysis Festschrift in Honour of Ben de Pagter (eds. G. Buskes, M. de Jeu, P. Dodds, A. Schep, F. Sukochev, J. van Neerven and A. Wickstead)
Koelink, H.T., Roman, P.M.
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Laguerre polynomial expansions
Journal of Computational and Applied Mathematics, 1995 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Analytical Solutions of the Driven Time‐Dependent Jaynes–Cummings Model
Annalen der Physik, EarlyView.Following the great strides made in the last decade towards the control and tunability of physical parameters in cavity quantum electrodynamics, this study presents new solutions to the dynamics of the time‐dependent Jaynes–Cummings model with variable external classical fields acting on the two‐level system and the quantized field mode.
Antonio Vidiella‐Barranco +5 more
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Matrix exceptional Laguerre polynomials
Studies in Applied Mathematics, 2023 AbstractWe give an analog of exceptional polynomials in the matrix‐valued setting by considering suitable factorizations of a given second‐order differential operator and performing Darboux transformations. Orthogonality and density of the exceptional sequence are discussed in detail. We give an example of matrix‐valued exceptional Laguerre polynomials
E. Koelink, L. Morey, P. Román
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Communications on Pure and Applied Mathematics, EarlyView.Abstract We consider a planar Coulomb gas ensemble of size N$N$ with the inverse temperature β=2$\beta =2$ and external potential Q(z)=|z|2−2clog|z−a|$Q(z)=|z|^2-2c \log |z-a|$, where c>0$c>0$ and a∈C$a \in \mathbb {C}$. Equivalently, this model can be realised as N$N$ eigenvalues of the complex Ginibre matrix of size (c+1)N×(c+1)N$(c+1) N \times (c+1)
Sung‐Soo Byun +2 more
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