Some generalized Jacobi polynomials

We give explicitly the recurrence coefficients in the three term recurrence relation of some generalized Jacobi polynomials defined by the positive weight (α,α + p;x,μ) = −μ(1−x2)α(1−x)p on [−1, +1]. The case p = 0 can be found in Chiharaʹs 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.