RECURRENCE-SHIFT RELATIONS FOR THE POLYNOMIAL FUNCTIONS OF ALDAYA, BISQUERT, AND NAVARRO-SALAS

Using a simple factorization scheme we obtain the recurrence-shift rel ations of the polynomial functions of Aldaya, Bisquert and Navarro-Sal as (ABNS), F-n(N)(omega/c root Nx), i.e., one-step first-order differe ntial relations referring to N, as follows. Firstly, we apply the sche me to the polynomial degree confirming the recurrence relations of Ald aya, Bisquert and Navarro-Salas but also obtaining another slightly mo dified pair. Secondly, the factorization scheme is applied to the Gege nbauer polynomials to get the recurrence relations with respect to the ir parameter. Next, we make use of Nagel's result, showing the connect ion between Gegenbauer polynomials and the ABNS functions, to write do wn the recurrence-shift relations for the latter ones. Such relations may be used in the study of the spatial structure of pair-creation pro cesses in an Anti-de Sitter gravitational background.