A new sequence of eigenfunctions is developed and studied in depth. These theta polynomials are derived from a recent analytic solution of the canonical Cauchy problem for parabolic equations, namely, the inverse heat conduction problem. By appealing to the methods of the operator calculus, it is possible to categorize the new functions as polynomials of binomial and Sheffer types. The connecti...

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 paper, we present a fast algorithm which evaluates a discrete Laplace transform with N points at M arbitrarily distributed points in C(N + M) work, where C depends only on the precision required. Our algorithm breaks even with the direct calculation at N = M = 20, and achieves a speedup of 1000 with 10000 points. It is based on a geometric divide and conquer strategy, combined with the ...

Se estudian perturbaciones de funcionales lineales (tanto en la recta real como en el ćırculo unidad) que pertenecen a la clase de Laguerre–Hahn. En particular, se obtiene una expresión para las funciones de Stieltjes y Carathéodory asociadas con los funcionales perturbados y se muestra que se preserva la clase de Laguerre–Hahn. Finalmente, se discute que bajo la transformación de Szegő la clas...

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 ...

A new algorithm for finding line spectral frequencies, LSF, is introduced, based on Laguerre method of root approximation. The method allows to assuredly find all roots one by one without recourse to polynomial deflation, which allows approximation to a high precision. Error bounds can be estimated by approximating from two sides with added margin. An improved variant of Laguerre recursion sche...

The cumulants and factorial moments of photon distribution for squeezed and correlated light are calculated in terms of Chebyshev, Legendre and Laguerre polynomials. The phenomenon of strong oscillations of the ratio of the cumulant to factorial moment is found. Running title: Oscillations of cumulants in squeezed states.

The connection between semi-classical orthogonal polynomials and discrete integrable systems is well established. The earliest example of a discrete integrable system in semi-classical orthogonal polynomials can be attributed first to Shohat in 1939 [16], then second by Freud [10] in 1976. However it wasn’t until the 1990’s, when the focus within integrable systems shifted from continuous to di...