Rate of Relative Growth of Orthogonal Polynomials

Let 0 < p < ∞ and ϵn = |an − a/2| + |bn − b| → 0. define a polynomial sequence {pn} by the recurrence relation xpn(x) = an + 1(x) + bnpn(x) + anpn − 1(x). It was proved that [formula] This paper investigates the rate of growth of such a sequence relative to its sums in terms of the rate of convergance of ϵn. Some applications to orthogonal polynomials are given.