Laurent continued fractions corresponding to pairs of power series (Q581700)

A continued fraction is said to correspond to two power series (one with positive, and one with negative powers), when expansions of approximants of the continued fraction agree in some sense with the first parts of the power series. This concept is considered for Laurent fractions, and it is shown that a one-to-one mapping between all such fractions and double sequences of real numbers exists, when the sequence satisfies the Hankel determinant condition. Further details are considered for subclasses of the Laurent fractions.