This reference - the proceedings of a research conference held in Loen, Norway - contains information on the analytic theory of continued fractions and their application to moment problems and orthogonal sequences of functions. Uniting the research efforts of many international experts, this volume: treats strong moment problems, orthogonal polynomials and Laurent polynomials, analyses sequences of linear fractional transformations, presents convergence results, including truncation error bounds, considers discrete distributions and limit functions arising from indeterminate moment problems, discusses Szego polynomials and their applications to frequency analysis, describes the quadrature formula arising from q-starlike functions, and covers continued fractional representations for functions related to the gamma function., This resource is intended for mathematical and numerical analysts, applied mathematicians, physicists, chemists, engineers, and upper-level undergraduate and agraduate students in these disciplines.