Closed-form sums for some perturbation series involving associated Laguerre polynomials

Infinite series sum_{n=1}^infty {(alpha/2)_n / (n n!)}_1F_1(-n, gamma, x^2), where_1F_1(-n, gamma, x^2)={n!_(gamma)_n}L_n^(gamma-1)(x^2), appear in the first-order perturbation correction for the wavefunction of the generalized spiked harmonic oscillator Hamiltonian H = -d^2/dx^2 + B x^2 + A/x^2 + lambda/x^alpha 0 0, A >= 0. It is proved that the series is convergent for all x > 0 and 2 gamma > alpha, where gamma = 1 + (1/2)sqrt(1+4A). Closed-form sums are presented for these series for the cases alpha = 2, 4, and 6. A general formula for finding the sum for alpha/2 = 2 + m, m = 0,1,2, ..., in terms of associated Laguerre polynomials, is also provided.Comment: 16 page

Test and commissioning of the CARLOS control boards for the ALICE Silicon Drift Detectors

This paper presents the test strategy employed during the installation of the CARLOS end ladder boards developed for the Silicon Drift Detectors (SDD) of ALICE. Each CARLOS board compresses the data provided by the front-end electronics of one SDD and sends them via an optical link of 800 Mbit/s to the data concentrator card (CARLOSrx) located in the counting room. The paper describes the integration of the CARLOS boards in the final SDD system, including its cooling and mechanical support, the power supply distribution and the optical interconnections. The results of the tests performed after each step of the installation sequence are reported

Su una classe di equazioni differenziali di primo ordine

L'autore considera quelle equazioni del tipo $\frac{dy}{dx} = a_0 + a_1y + ... + a_ny^n$, a coefficienti funzioni di $x$, che si trasformano in altre a coefficienti costanti mediante sostituzioni lineari, allo scopo di perfezionare e confrontare noti risultati e di ricavarne altri

Relazioni tra polinomi ultrasferici di Laguerre e di Hermite

L'autore stabilisce due relazioni che legano i polinomi ultrasferici a quelli di Laguerre e di Hermite. E ne deduce altre particolari sui soli polinomi di Hermite