Ordered OLPS and CF Nth numerators Original Research Article

Definitions, theorems and examples are established for a general model of Laurent polynomial spaces and ordered orthogonal Laurent polynomial sequences, ordered with respect to ordered bases and orthogonal with respect to inner products image decomposed into transition functional circled dot operator and strong moment functional, or, more generally, sample functional image couplings. Under this formulation that is shown to subsume those in the existing literature, new fundamental results are produced, including necessary and sufficient conditions for ordered OLPS to be sequences of nth numerators of continued fractions, in contrast to the classical result concerning nth denominators which is shown to hold only in special cases.