Consider a (nonnegative) measure d sigma with support in the interval
[a, b] such that the respective orthogonal polynomials, above a
specific index l, satisfy a three-term recurrence relation with constant
coefficients. We show that the corresponding Stieltjes polynomials,
above the index 2l - 1, have a very simple and useful representation in
terms of the orthogonal polynomials. As a result of this, the
Gauss-Kronrod quadrature formulae for da have all the desirable
properties, namely, the interlacing of nodes, their inclusion in the
closed interval [a,b] (under an additional assumption on d sigma), and
the positivity of all weights. Furthermore, the interpolatory quadrature
formulae based on the zeros of the Stieltjes polynomials have positive
weights, and both of these quadrature formulae have elevated degrees of
exactness
