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Continued Fractions: From Analytic Number Theory to Constructive Approximation: A Volume in Honor of L. J. Lange
Edited by: Bruce C. Berndt, University of Illinois, Urbana, IL, and Fritz Gesztesy, University of Missouri, Columbia, MO

Contemporary Mathematics
1999; 379 pp; softcover
Volume: 236
ISBN-10: 0-8218-1200-9
ISBN-13: 978-0-8218-1200-6
List Price: US$90
Member Price: US$72
Order Code: CONM/236
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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, Padé 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.


Graduate students, research mathematicians, and physicists interested in number theory, approximation theory, and related fields.

Table of Contents

  • R. Askey -- Continued fractions and orthogonal polynomials
  • B. C. Berndt, Y.-S. Choi, and S.-Y. Kang -- The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society
  • B. Bojanov and A. S. Ranga -- Some examples of moment preserving approximation
  • C. F. Bracciali -- Relations between certain symmetric strong Stieltjes distributions
  • A. Bultheel, C. Díaz-Mendoza, P. González-Vera, and R. Orive -- Estimates of the rate of convergence for certain quadrature formulas on the half-line
  • A. Bultheel and P. González-Vera -- Wavelets by orthogonal rational kernels
  • H. H. Chan and V. Tan -- On the explicit evaluations of the Rogers-Ramanujan continued fraction
  • D. Chelst -- Absence of phase transitions in modified two-component plasmas: The analytic theory of continued fractions in statistical mechanics
  • M. E. H. Ismail and D. R. Masson -- Some continued fractions related to elliptic functions
  • W. B. Jones and G. Shen -- Asymptotics of Stieltjes continued fraction coefficients and applications to Whittaker functions
  • L. J. Lange -- A generalization of Van Vleck's theorem and more on complex continued fractions
  • X. Li -- Convergence of interpolating Laurent polynomials on an annulus
  • L. Lorentzen -- Convergence criteria for continued fractions K\((a_n/1)\) based on value sets
  • O. Njåstad -- Strong Stieltjes moment problems
  • F. Peherstorfer and R. Steinbauer -- Weak asymptotics of orthogonal polynomials on the support of the measure of orthogonality and considerations on functions of the second kind
  • S. Perrine -- Trees of approximation constants
  • I. Rodnianski -- Continued fractions and Schrödinger evolution
  • W. Van Assche -- Multiple orthogonal polynomials, irrationality and transcendence
  • A. J. van der Poorten -- Reduction of continued fractions of formal power series
  • H. Waadeland -- Some observations in frequency analysis
  • F. Wielonsky -- Some properties of Hermite-Padé approximants to \(e^z\)
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