On co-recursive orthogonal polynomials
Theodore S. Chihara · Proceedings of the American Mathematical Society · 1957
Pt(x) = (X + bn)P*n-l(x) - X„P!_2(x), K = 2, 3, • • • where P0*(x) = l, P*(x) =Pi(x) — c. We then seek to determine the properties of the P*(x) from those of the P„(x). In order to have orthogonal polynomials, we will restrict c to be real. 2. Some formal relations. Since P„(x) and P*(x) satisfy identical recurrence formulas, except for initial conditions, it follows that P*(x) —P„(x) also satisfies (1.1) together with the initial conditions, Pt(x) -Po(x) =0, P?(x) -Pi(x) = -c. Therefore we have1