where , and are constants. Also denote
where the bar again signifies compex conjugate. Then
Assume that . Set
Let and , , be OP’s with weight functions and , respectively, on . Then
where , , , and are independent of .
See Baxter (1961) for general theory. See Askey (1982) and Pastro (1985) for special cases extending (18.33.13)–(18.33.14) and (18.33.15)–(18.33.16), respectively. See Gasper (1981) and Hendriksen and van Rossum (1986) for relations with Laurent polynomials orthogonal on the unit circle. See Al-Salam and Ismail (1994) for special biorthogonal rational functions on the unit circle.