Results 1 to 10 of about 2,012 (183)
The centralizer of the Laguerre polynomial set [PDF]
Rocky Mountain Journal of Mathematics, 1979 The set \(\pi\) of all simple polynomial sets with umbral product is a noncommutative group with the identity \(I=\{x^ n,\quad n=0,1,2,...\}.\) The authors have studied the characterization of the elements of the centralizer \(C_{\pi}(L^{\alpha})\) of the Laguerre polynomial set in the group \(\pi\). Four special cases have also been considered.
Nadhla A. Al-Salam, W. A. Al‐Salam
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Hermite and Laguerre 2D polynomials
Journal of Computational and Applied Mathematics, 2001 The Hermite \(2D\) polynomials \(H_{m,n} (U;x,y)\) and Laguerre \(2D\) polynomials \(L_{m,n} (U;z,\overline z)\) are defined as functions of two variables with an arbitrary \(2D\) matrix \(U\) as parameter. Their properties are discussed, explicit representations are given and recursion relations and generating functions for these polynomials are ...
Alfred Wünsche
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A note on the Laguerre polynomials. [PDF]
Michigan Mathematical Journal, 1960 L. Carlitz
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Bounds for zeros of the Laguerre polynomials
Journal of Approximation Theory, 2003 The author shows that the least and largest zeros \(x_1, x_n\) of the Laguerre polynomial \(L_n ^{(\alpha)}(x)\) satisfies \[ x_1 > s-r + {(s-r)^{2/3} \over 2r^{1/3}} \] \[ x_n < s+r + {(s+r)^{2/3} \over 2r^{1/3}} \] with \[ s=2n+ \alpha +1, \;r= \sqrt{4n^2 +(2n-1)(2 \alpha +2)} \] provided \(n\geq 7, \alpha \geq 8\).
Ilia Krasikov
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Asymptotic Forms for Laguerre Polynomials [PDF]
Proceedings of the American Mathematical Society, 1970 Benjamin Muckenhoupt
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Integrals of Products of Laguerre Polynomials [PDF]
Mathematics of Computation, 1960 R. D. Lord
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Exceptional Laguerre Polynomials [PDF]
Studies in Applied Mathematics, 2018 AbstractThe aim of this paper is to present the construction of exceptional Laguerre polynomials in a systematic way and to provide new asymptotic results on the location of the zeros. To describe the exceptional Laguerre polynomials, we associate them with two partitions.
Niels Bonneux, Arno B.J. Kuijlaars
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Products of Laguerre Polynomials [PDF]
Mathematics of Computation, 1960 and, in particular, is symmetric in r, s, t. A closed formula has been obtained for Cry by Watson [41. We begin by obtaining the same formula by a very simple argument. In ? wce (lerive a simple recurrence relation suitable for rapidly generating the coefficients as needed when working with a high speed computing machine.
George H. Weiss, Joseph Gillis
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Laguerre polynomials of derivations [PDF]
Israel Journal of Mathematics, 2014 We introduce a 'grading switching' for arbitrary nonassociative algebras of prime characteristic p, aimed at producing a new grading of an algebra from a given one. We take inspiration from a fundamental tool in the classification theory of modular Lie algebras known as 'toral switching', which relies on a delicate adaptation of the exponential of a ...
AVITABILE, MARINA, Mattarei, S.
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Efficient computation of Laguerre polynomials [PDF]
Computer Physics Communications, 2017 To appear in Computer Physics ...
Nico M. Temme +4 more
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