Orthogonal Laurent-polynomials and continued fractions associated with log-normal distributions

摘要

This paper describes properties and computational procedures related to orthogonal Laurent-polynomials, continued fractions, two-point Padé approximants, strong moment problems and L-Gaussian quadrature associated with log-normal distribution functions φ(t) defined by φ′(t) = (q1/2/2ϰ√π) e−(lnt/2ϰ)2, 0 < q < 1, q = e−2ϰ2. Log-normal distributions have recently been found to be applicable in weather research related to hurricanes. They are also of particular interest since one can obtain many explicit expressions for associated functions, formulae and other constructions.