Abstract:In this contribution we obtain some algebraic properties associated with the sequence of polynomials orthogonal with respect to the Sobolev-type inner product:p,qs=∫Rp(x)q(x)dμ(x)+M0p(0)q(0)+M1p′(0)q′(0), where p,q are polynomials, M0, M1 are non-negative real numbers and μ is a symmetric positive measure. These include a five-term recurrence relation, a three-term recurrence relation with rational coefficients, and an explicit expression for its norms. Moreover, we use these results to deduce asymptotic prope… Show more
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