The ensemble average of $| \sum_{j=1}^N e^{i k \lambda_j} |^2$ is interest as a probe quantum chaos, its connected part, the structure function. Plotting this for model systems chaotic spectra reveals what has been termed dip-ramp-plateau shape. Generalising earlier work Br\'ezin and Hikami Gaussian unitary ensemble, it shown how in case Laguerre can be reduced to an expression involving spectr...

A Laguerre-Galerkin method is proposed and analyzed for the Burgers equation and Benjamin-Bona-Mahony (BBM) equation on a semiinfinite interval. By reformulating these equations with suitable functional transforms, it is shown that the Laguerre-Galerkin approximations are convergent on a semi-infinite interval with spectral accuracy. An efficient and accurate algorithm based on the Laguerre-Gal...

Kleinewillinghöfer classified Laguerre planes with respect to central automorphisms. Polster and Steinke investigated flat Laguerre planes and their so-called Kleinewillinghöfer types, that is, the Kleinewillinghöfer types with respect to the full automorphism group. For some of these types the existence question remained open. We provide strong necessary existence conditions for flat Laguerre ...

We establish a large n complete asymptotic expansion for q-Laguerre polynomials and a complete asymptotic expansion for a q-Bessel function of large argument. These expansions are needed in our study of an exactly solvable random transfer matrix model for disordered electronic systems. We also give a new derivation of an asymptotic formula due to Littlewood (1907).

In this paper, we consider the discrete Laguerre polynomials [Formula: see text] orthogonal with respect to weight function supported on infinite nodes text]. We focus “band-saturated region” situation when parameter As text], uniform expansions for are achieved in different regions complex plane. Typically, Airy-function and Gamma-function derived near endpoints of band origin, respectively. T...

Abstract.In this paper, the generalized Bessel matrix polynomials are introduced, starting from the hypergeometric matrix function. Integral form, Rodrigues’s formula and generating matrix function are then developed for the generalized Bessel matrix polynomials. These polynomials appear as finite series solutions of second-order matrix differential equations and orthogonality property for the ...