named generalized Laguerre polynomials, as will be done here (alternatively associated Laguerre polynomials or, rarely, Sonine polynomials, after their inventor...
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the q-Laguerre polynomials, or generalized Stieltjes–Wigert polynomials P(α) n(x;q) are a family of basic hypergeometric orthogonal polynomials in the...
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to define the multidimensional polynomials. Like the other classical orthogonal polynomials, the Hermite polynomials can be defined from several different...
57 KB (10,024 words) - 18:31, 4 August 2024
orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as...
35 KB (6,102 words) - 20:33, 17 November 2022
zeros and Gaussian Weights of certain Associated Laguerre Polynomials and the related Hermite Polynomials". Mathematics of Computation. 18 (88): 598–616...
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In mathematics, the big q-Laguerre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter...
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orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The...
14 KB (2,027 words) - 17:16, 30 September 2024
In mathematics, the continuous q-Laguerre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek...
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the little q-Laguerre polynomials pn(x;a|q) or Wall polynomials Wn(x; b,q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey...
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Gaussian beam (redirect from Laguerre-Gaussian)
using the Laguerre-Gaussian modal decomposition. These functions are written in cylindrical coordinates using generalized Laguerre polynomials. Each transverse...
47 KB (6,956 words) - 12:32, 18 September 2024
Confluent hypergeometric function (section Connection with Laguerre polynomials and similar representations)
the sine integral, logarithmic integral Hermite polynomials Incomplete gamma function Laguerre polynomials Parabolic cylinder function (or Weber function)...
24 KB (4,566 words) - 19:59, 11 August 2024
mathematics, Laguerre transform is an integral transform named after the mathematician Edmond Laguerre, which uses generalized Laguerre polynomials L n α (...
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investigated orthogonal polynomials (see Laguerre polynomials). Laguerre's method is a root-finding algorithm tailored to polynomials. He laid the foundations...
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In mathematics, the Tricomi–Carlitz polynomials or (Carlitz–)Karlin–McGregor polynomials are polynomials studied by Tricomi (1951) and Carlitz (1958) and...
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functions in terms of the Bessel–Clifford function. In terms of the Laguerre polynomials Lk and arbitrarily chosen parameter t, the Bessel function can be...
71 KB (11,604 words) - 17:02, 12 October 2024
up the Legendre polynomials as one of the three classical orthogonal polynomial systems. The other two are the Laguerre polynomials, which are orthogonal...
31 KB (5,593 words) - 16:46, 16 October 2024
In mathematics, the affine q-Krawtchouk polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by...
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Koornwinder polynomials Kostka polynomial Kravchuk polynomials Laguerre polynomials Laurent polynomial Linearised polynomial Littlewood polynomial Legendre...
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number, the solutions of this equations are generalized (associated) Laguerre polynomials g ( x ) = L k ( ℓ + 1 2 ) ( x ) . {\displaystyle g(x)=L_{k}^{\scriptscriptstyle...
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quadrature Legendre polynomials Spherical harmonics Whipple's transformation of Legendre functions Laguerre polynomials Hermite polynomials Courant & Hilbert...
31 KB (5,475 words) - 23:52, 6 March 2024
Plancherel–Rotach asymptotics (category Orthogonal polynomials)
asymptotics for the Hermite polynomial and Laguerre polynomial. Nowadays asymptotic expansions of this kind for orthogonal polynomials are referred to as Plancherel–Rotach...
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\ell } and order m {\displaystyle m} . Note that the generalized Laguerre polynomials are defined differently by different authors. The usage here is consistent...
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polynomials Lucas polynomials Spread polynomials Touchard polynomials Rook polynomials Polynomial sequences of binomial type Orthogonal polynomials Secondary...
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Lah number (section Link to Laguerre polynomials)
{6}{x^{5}}}+{\frac {1}{x^{6}}}\right)\cdot e^{\frac {1}{x}}} Generalized Laguerre polynomials L n ( α ) ( x ) {\displaystyle L_{n}^{(\alpha )}(x)} are linked to...
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Konhauser polynomials, introduced by Konhauser (1967), are biorthogonal polynomials for the distribution function of the Laguerre polynomials. Konhauser...
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Hermite polynomials and Laguerre polynomials are examples of Brenke polynomials, and asked if there are any other sequences of orthogonal polynomials of this...
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In mathematics, Meixner polynomials (also called discrete Laguerre polynomials) are a family of discrete orthogonal polynomials introduced by Josef Meixner (1934)...
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In numerical analysis, Laguerre's method is a root-finding algorithm tailored to polynomials. In other words, Laguerre's method can be used to numerically...
11 KB (1,783 words) - 15:46, 4 September 2024
The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)} and...
61 KB (11,472 words) - 09:09, 5 September 2024
Orthogonal functions (section Polynomials)
{\displaystyle \langle f,g\rangle =\int w(x)f(x)g(x)\,dx.} For Laguerre polynomials on ( 0 , ∞ ) {\displaystyle (0,\infty )} the weight function is w...
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