We describe the behavior as n → ∞ of the Laplace transforms of Pn, where P a fixed complex polynomial. As a consequence we obtain a new elementary proof of an result of Gillis-Ismail-Offer [2] in the combinatorial theory of derangements. 1 Statement of the main results The generalized derangement problem in combinatorics can be formulated as follows. Suppose X is a finite set and ∼ is an equiva...

In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...

This paper presents a series of new results in modeling of the Grünwald-Letnikov discretetime fractional difference by means of discrete-time Laguerre filers. The introduced Laguerrebased difference LD and combined fractional/Laguerre-based difference CFLD are shown to perfectly approximate its fractional difference original, for fractional order α ∈ 0, 2 . This paper is culminated with the pre...

During the mode transition from the pure electric propulsion mode to the hybrid propulsion mode, clutch-based pre-transmission parallel hybrid electric vehicles are subject to drivability issues. These issues originate from the fact that in the clutch-based pre-transmission parallel hybrid powertrain (CPPHP) configuration, the clutch connects the engine and the motor. Without a carefully design...

Using chain sequences we formulate a procedure to find upper (lower) bounds for the largest (smallest) zero of orthogonal polynomials in terms of their recurrence coefficients. We also apply our method to derive bounds for extreme zeros of the Laguerre, associated Laguerre, Meixner, and MeixnerPollaczek polynomials. In addition, we consider bounds for the extreme zeros of Jacobi polynomials of ...

In this work, we propose a numerical method to obtain an unconditionally stable solution for the finite-difference time-domain (FDTD) method for the TE case. This new method does not utilize the customary explicit leapfrog time scheme of the conventional FDTD method. Instead we solve the time-domain Maxwell’s equations by expressing the transient behaviors in terms of weighted Laguerre polynomi...

We show how Viennot’s combinatorial theory of orthogonal polynomials may be used to generalize some recent results of Sukumar and Hodges on the matrix entries in powers of certain operators in a representation of su(1, 1). Our results link these calculations to finding the moments and inverse polynomial coefficients of certain Laguerre polynomials and Meixner polynomials of the second kind. As ...

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...

Using Casorati determinants of Meixner polynomials (m n )n , we construct for each pair F = (F1, F2) of finite sets of positive integers a sequence of polynomials ma,c;F n , n ∈ σF , which are eigenfunctions of a second order difference operator, where σF is certain infinite set of nonnegative integers, σF N. When c and F satisfy a suitable admissibility condition, we prove that the polynomials...