Abstract
We give explicitly the recurrence coefficients in the three term recurrence relation of some generalized Jacobi polynomials defined by the positive weight rho(alpha, alpha + p; x, mu) \x\(-mu) (1 - x(2))(alpha) (1 - x)(p) on [-1, +1]. The case p = 0 can be found in Chihara's book. The case p = 1 is treated by the first author, and we consider here the cases p = 2, 3, 4. These recurrence coefficients can be used to prove that their corresponding polynomials are random walk and then are of interest in birth and death process [1,2]; for instance, the cases p = 1, 2 are treated. (C) 2003 Elsevier Science Ltd. All rights reserved.