On Freud-Sobolev type orthogonal polynomials

In this contribution we deal with sequences of monic polynomials orthogonal with respect to the Freud Sobolev-type inner product
⟨p,q⟩1=∫Rp(x)q(x)e−x4dx+M0p(0)q(0)+M1p′(0)q′(0),
where p, q are polynomials, M0 and M1 are nonnegative real numbers. Connection formulas between these polynomials and Freud polynomials are deduced and, as an application, an algorithm to compute their zeros is presented. The location of their zeros as well as their asymptotic behavior is studied. Finally, an electrostatic interpretation of them in terms of a logarithmic interaction in the presence of an external field is given.

orthogonal polynomials; exponential weights; freud-sobolev type orthogonal polynomials; zeros; interlacing; electrostatic interpretation; zeros; asymptotics

On Freud-Sobolev type orthogonal polynomials Articles