# Continued Fractions: From Analytic Number Theory to Constructive Approximation: A Volume in Honor of L. J. Lange

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*Bruce C. Berndt; Fritz Gesztesy*

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.

#### Readership

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

# Table of Contents

## Continued Fractions: From Analytic Number Theory to Constructive Approximation: A Volume in Honor of L. J. Lange

- Contents vii8 free
- Preface and Dedication ix10 free
- List of Participants xvi17 free
- Continued fractions and orthogonal polynomials 120 free
- The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society 1534
- Some examples of moment preserving approximation 5776
- Relations between certain symmetric strong Stieltjes distributions 7190
- Estimates of the rate of convergence for certain quadrature formulas on the half-line 85104
- Wavelets by orthogonal rational kernels 101120
- On the explicit evaluations of the Rogers-Ramanujan continued fraction 127146
- Absence of phase transitions in modified two-component plasmas: The analytic theory of continued fractions in statistical mechanics 137156
- Some continued fractions related to elliptic functions 149168
- Asymptotics of Stieltjes continued fraction coefficients and applications to Whittaker functions 167186
- A generalization of Van Vleck's theorem and more on complex continued fractions 179198
- Convergence of interpolating Laurent polynomials on an annulus 193212
- Convergence criteria for continued fractions K(an/1) based on value sets 205224
- Strong Stieltjes moment problems 257276
- Weak asymptotics of orthogonal polynomials on the support of the measure of orthogonality and considerations on functions of the second kind 277296
- Trees of approximation constants 297316
- Continued fractions and Schrödinger evolution 311330
- Multiple orthogonal polynomials, irrationality and transcendence 325344
- Reduction of continued fractions of formal power series 343362
- Some observations in frequency analysis 357376
- Some properties of Hermite–Padé approximants to ez 369388