Orthogonal moments (Q1178590)

Using a result due to H. L. Krall on the equivalence of a certain type of recurrence relation for the moments \(\{c_ n(t)\}\) (\(t\) a parameter) and the differential equation for the orthogonal polynomials having \(\{c_ n(t)\}\) as its moment sequence, the authors give in this nice paper an extensive study of the OPS-s that are generated by moment sequences of which the elements themselves are orthogonal polynomials. They cover all moment sequences where Krall's result is applicable: Laguerre, Hermite, ultraspherical, Charlier and Meixner (I \& II) leading to resp. Bessel, Hermite, ultraspherical, Laguerre and Jacobi polynomials. Explicit formulae are given for the Hankel determinants (called Turanians while the moments form an OPS), along with information on total positivity of the moment sequences.