Relative Asymptotics for Orthogonal Polynomials with a Sobolev Inner Product Original Research Article

We investigate orthogonal polynomials for a Sobolev type inner product 〈ƒ, g〉 = (ƒ, g) + λƒ′(c) g′(c), where (ƒ, g) is an ordinary inner product in L2(μ) with μ a positive measure on the real line. We compare the Sobolev orthogonal polynomials with the orthogonal polynomials corresponding to the measure μ and analyse the five-term recurrence relation for the Sobolev orthogonal polynomials.