Asymptotics of Kissing Polynomials and their Recurrence Relations

Kissing polynomials, dubbed so for the peculiar behavior of their zeros, are a family of polynomials orthogonal with respect to an oscillatory, complex-valued weight. These polynomials were first considered in the development of a Gaussian quadrature rule to address highly oscillatory integrals. Since the weight of orthogonality is complex-valued, the quadrature nodes are not necessarily restricted to the real line, nor are we guaranteed n nodes. In this talk, I will introduce these kissing polynomials and discuss several results about the asymptotic behavior of the polynomials and their recurrence coefficients. [arXiv:2101.04147]