An example of nonsymmetric semi-classical form of class s=1; generalization of a case of Jacobi sequence

Abstract

We give explicitly the recurrence coefficients of a nonsymmetric semi-classical sequence of polynomials of class s=1. This sequence generalizes the Jacobi polynomial sequence, that is, we give a new orthogonal sequence {Pˆn(α,α+1)(x,μ)}, where μ is an arbitrary parameter with ℜ(1−μ)>0 in such a way that for μ=0 one has the well-known Jacobi polynomial sequence {Pˆn(α,α+1)(x)}, n≥0.