The tensor product of a positive and a negative discrete series representation of the quantum algebra Uq ( su(1, 1) ) decomposes as a direct integral over the principal unitary series representations. Discrete terms can appear, and these terms are a finite number of discrete series representations, or one complementary series representation. From the interpretation as overlap coefficients of li...

—An explicit formula for the Fourier coef cients of the Legendre polynomials can be found in the Bateman Manuscript Project. However, formulas for more general classes of orthogonal polynomials do not appear to have been worked out. Here we derive explicit formulas for the Fourier series of Gegenbauer, Jacobi, Laguerre and Hermite polynomials. The methods described here apply in principle to an...

The Burgers’ equation with uncertain initial and boundary conditions is investigated using a Polynomial Chaos (PC) expansion approach where the solution is represented as a truncated series of stochastic, orthogonal polynomials. The analysis of well posedness for the system resulting after Galerkin projection is presented and follows the pattern of the corresponding deterministic Burgers equati...

We study the contribution of a truncated BFKL Pomeron series to the hadronic processes showing that a reliable description is obtained using two orders in perturbation theory. The pp(pp̄) total cross sections are described with good agreement, consistent with the unitarity bound. We also calculate the elastic scattering amplitude at non zero momentum transfer t, introducing two distinct ansätze ...

We study the contribution of the truncated BFKL Pomeron series to the electroproduction process showing that a reliable description is obtained taking into account two orders in perturbation theory. Using the recent F2 logarithmic slope data as a constraint to the adjustable parameters, the inclusive structure function is described in a wide range of the small x HERA kinematical region, consist...

In this paper we address the problem of approximating functions on a semi-in nite interval by truncated series of orthonormal generalized Laguerre functions. The generalized Laguerre functions contain two parameters, namely a scale factor and an order of generalization. The rate of convergence of a generalized Laguerre series depends on the choice of these parameters. Results concerning the det...