The authors consider sequences of Laurent polynomials where
A linear functional L determined by is defined as for and for . Propositions and theorems are proved that link the existence of L, and three- term linear recurrence relations for the Q’s and thereby general T- fractions.
A sequence of lacunary Laurent polynomials is introduced orthogonal with relation to where , . Applications are made to ratios of hypergeometric functions. Orthogonal Laurent polynomials were introduced in W. B. Jones and W. J. Thron [Analytic theory of continued fractions, Proc. Sem. Workshop, Loen/Norw. 1981, Lect. Notes Math. 932, 4-37 (1982; Zbl 0508.30008)] and further developed in O. Njåstad and W. J. Thron, Skr., K. Nor. Vidensk. Selsk. (1983).