Some new results for chain-sequence polynomials

We study the class C of (generalized) orthogonal polynomial sequences {Pn(x)}n=0∞ satisfying a recurrence relation of the type Pn(x) = (x − cn)Pn−1(x) − λnPn−2(x), n > 1, where λn ≠ 0 and the sequence {λn+1(cncn+1)}n=1∞ constitutes a chain sequence. We obtain a new characterization of C in terms of the moment sequence associated with an orthogonal polynomial sequence, and contribute to the solution of the problem of determining a (signed) orthogonalizing measure for a member of C.