named generalized Laguerre polynomials, as will be done here (alternatively associated Laguerre polynomials or, rarely, Sonine polynomials, after their inventor...

to define the multidimensional polynomials. Like the other classical orthogonal polynomials, the Hermite polynomials can be defined from several different...

orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as...

zeros and Gaussian Weights of certain Associated Laguerre Polynomials and the related Hermite Polynomials". Mathematics of Computation. 18 (88): 598–616...

orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The...

using the Laguerre-Gaussian modal decomposition. These functions are written in cylindrical coordinates using generalized Laguerre polynomials. Each transverse...

investigated orthogonal polynomials (see Laguerre polynomials). Laguerre's method is a root-finding algorithm tailored to polynomials. He laid the foundations...

the sine integral, logarithmic integral Hermite polynomials Incomplete gamma function Laguerre polynomials Parabolic cylinder function (or Weber function)...

up the Legendre polynomials as one of the three classical orthogonal polynomial systems. The other two are the Laguerre polynomials, which are orthogonal...

In mathematics, the big q-Laguerre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter...

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...

the q-Laguerre polynomials, or generalized Stieltjes–Wigert polynomials P(α) n(x;q) are a family of basic hypergeometric orthogonal polynomials in the...

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...

polynomials Lucas polynomials Spread polynomials Touchard polynomials Rook polynomials Polynomial sequences of binomial type Orthogonal polynomials Secondary...

\ell } and order m {\displaystyle m} . Note that the generalized Laguerre polynomials are defined differently by different authors. The usage here is consistent...

Koornwinder polynomials Kostka polynomial Kravchuk polynomials Laguerre polynomials Laurent polynomial Linearised polynomial Littlewood polynomial Legendre...

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...

In mathematics, the continuous q-Laguerre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek...

quadrature Legendre polynomials Spherical harmonics Whipple's transformation of Legendre functions Laguerre polynomials Hermite polynomials Courant & Hilbert...

In mathematics, Meixner polynomials (also called discrete Laguerre polynomials) are a family of discrete orthogonal polynomials introduced by Josef Meixner (1934)...

mathematics, Laguerre transform is an integral transform named after the mathematician Edmond Laguerre, which uses generalized Laguerre polynomials L n α (...

{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...

polynomials q-Krawtchouk polynomials q-Laguerre polynomials q-Meixner polynomials q-Meixner–Pollaczek polynomials q-Racah polynomials Gaussian q-distribution...

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...

In mathematics, the Tricomi–Carlitz polynomials or (Carlitz–)Karlin–McGregor polynomials are polynomials studied by Tricomi (1951) and Carlitz (1958) and...

asymptotics for the Hermite polynomial and Laguerre polynomial. Nowadays asymptotic expansions of this kind for orthogonal polynomials are referred to as Plancherel–Rotach...

{\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...

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...

{L_{k}}^{(l+{1 \over 2})}(2\nu r^{2})} are generalized Laguerre polynomials; The order k of the polynomial is a non-negative integer; Y l m ( θ , ϕ ) {\displaystyle...

Hermite polynomials and Laguerre polynomials are examples of Brenke polynomials, and asked if there are any other sequences of orthogonal polynomials of this...