Abstract:
The zeros of quasi-orthogonal polynomials play a key role in applications
in areas such as interpolation theory, Gauss-type quadrature
formulas, rational approximation and electrostatics. We extend previous
results on the quasi-orthogonality of Jacobi polynomials and
discuss the quasi-orthogonality of Meixner–Pollaczek, Hahn, Dual-
Hahn and Continuous Dual-Hahn polynomials using a characterization
of quasi-orthogonality due to Shohat. Of particular interest are
the Meixner–Pollaczek polynomials whose linear combinations only
exhibit quasi-orthogonality of even order. In some cases, we also
investigate the location of the zeros of these polynomials for quasiorthogonality
of order 1 and 2 with respect to the end points of
the interval of orthogonality, as well as with respect to the zeros of
different polynomials in the same orthogonal sequence.
