We develop an extension of the classical Bell polynomials introducing the Laguerre-type version of this well-known mathematical tool. The Laguerre-type Bell polynomials are useful in order to compute the nth Laguerre-type derivatives of a composite function. Incidentally, we generalize a result considered by L. Carlitz in order to obtain explicit relationships between Bessel functions and gener...

Let Cλ n(x), n = 0, 1, . . . , λ > −1/2, be the ultraspherical (Gegenbauer) polynomials, orthogonal in (−1, 1) with respect to the weight function (1−x2)λ−1/2. Denote by xnk(λ), k = 1, . . . , n, the zeros of Cλ n(x) enumerated in decreasing order. In this short note we prove that, for any n ∈ IN , the product (λ+1)xn1(λ) is a convex function of λ if λ ≥ 0. The result is applied to obtain some ...

We investigate a numerical solution of the flavor-nonsinglet Altarelli-Parisi equation with next-to-leading-order α s corrections by using Laguerre polynomials. Expanding a structure function (or a quark distribution) and a splitting function by the Laguerre polynomials, we reduce an integrodifferential equation to a summation of finite number of Laguerre coefficients. We provide a FORTRAN prog...

Laguerre filters constitute an orthonormal basis for the Hilbert space, for this they are used in system identification and reduced-order modelling. In this paper a new property of Laguerre filters is introduced: it is shown that the system having as transfer function the sum of the first n + 1 functions has all the singular values equals each other. On the basis of this property a generalizati...

A Laguerre minimal surface is an immersed surface in R being an extremal of the functional ∫ (H/K− 1)dA. In the present paper, we prove that any ruled Laguerre minimal surface distinct from a plane is up to motion a convolution of the helicoid x = y tan z, the cycloid r(t) = (t− sin t, 1−cos t, 0) and the Plücker conoid (ax+ by) = z(x+y) for some a, b ∈ R. To achieve invariance under Laguerre t...

Abstract In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|e 2/2, β ≥ 0, x ∈ R. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted ge...

We calculate the Wigner distribution function for the Calogero-Sutherland system which consists of harmonic and inverse-square interactions. The Wigner distribution function is separated out into two parts corresponding to the relative and center-of-mass motions. A general expression for the relative Wigner function is obtained in terms of the Laguerre polynomials by introducing a new identity ...

In this correspondence, we point out two typographical errors in Chai and Tjhung’s paper and we offer the correct formula of the unified Laguerre polynomial-seriesbased cumulative distribution function (cdf) for small-scale fading distributions. A Laguerre polynomial-series-based cdf formula for non-central chi-square distribution is also provided as a special case of our unified cdf result.

A phase-space description of the Laguerre-Gaussian modes is presented that points out the connection between these modes and the Hermite-Gaussian modes. We exploit the underlying phase-space symmetries to derive a closed-form expression for the Wigner distribution function of Laguerre-Gaussian modes. This expression is as compact as the one for the Hermite-Gaussian modes.