This volume presents the contributions from the international conference held at the University of Missouri at Columbia, marking Professor Lange's 70th birthday and his retirement from the university. The principal purpose of the conference was to focus on continued fractions as a common interdisciplinary theme bridging gaps between a large number of fields - from pure mathematics to mathematical physics and approximation theory. Evident in this work is the widespread influence of continued fractions in a broad range of areas of mathematics and physics, including number theory, elliptic functions, Pade approximations, orthogonal polynomials, moment problems, frequency analysis, and regularity properties of evolution equations. Different areas of current research are represented. The lectures at the conference and the contributions to this volume reflect the wide range of applicability of continued fractions in mathematics and the applied sciences.
Continued fractions and orthogonal polynomials by R. Askey The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society by B. C. Berndt, Y.-S. Choi, and S.-Y. Kang Some examples of moment preserving approximation by B. Bojanov and A. S. Ranga Relations between certain symmetric strong Stieltjes distributions by C. F. Bracciali Estimates of the rate of convergence for certain quadrature formulas on the half-line by A. Bultheel, C. Diaz-Mendoza, P. Gonzalez-Vera, and R. Orive Wavelets by orthogonal rational kernels by A. Bultheel and P. Gonzalez-Vera On the explicit evaluations of the Rogers-Ramanujan continued fraction by H. H. Chan and V. Tan Absence of phase transitions in modified two-component plasmas: The analytic theory of continued fractions in statistical mechanics by D. Chelst Some continued fractions related to elliptic functions by M. E. H. Ismail and D. R. Masson Asymptotics of Stieltjes continued fraction coefficients and applications to Whittaker functions by W. B. Jones and G. Shen A generalization of Van Vleck's theorem and more on complex continued fractions by L. J. Lange Convergence of interpolating Laurent polynomials on an annulus by X. Li Convergence criteria for continued fractions K$(a n/1)$ based on value sets by L. Lorentzen Strong Stieltjes moment problems by O. Njastad Weak asymptotics of orthogonal polynomials on the support of the measure of orthogonality and considerations on functions of the second kind by F. Peherstorfer and R. Steinbauer Trees of approximation constants by S. Perrine Continued fractions and Schrodinger evolution by I. Rodnianski Multiple orthogonal polynomials, irrationality and transcendence by W. Van Assche Reduction of continued fractions of formal power series by A. J. van der Poorten Some observations in frequency analysis by H. Waadeland Some properties of Hermite-Pade approximants to $e^z$ by F. Wielonsky.