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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
Fritz Gesztesy University of Missouri, Columbia, MO
Continued Fractions: From Analytic Number Theory to Constructive Approximation
eBook ISBN:  978-0-8218-7827-9
Product Code:  CONM/236.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Continued Fractions: From Analytic Number Theory to Constructive Approximation
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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
Fritz Gesztesy University of Missouri, Columbia, MO
eBook ISBN:  978-0-8218-7827-9
Product Code:  CONM/236.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 2361999; 379 pp
    MSC: Primary 42; 30; 40; Secondary 11; 33; 41

    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
     
     
    • Articles
    • Richard Askey — Continued fractions and orthogonal polynomials [ MR 1665360 ]
    • Bruce C. Berndt, Youn-Seo Choi and Soon-Yi Kang — The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society [ MR 1665361 ]
    • B. Bojanov and A. Sri Ranga — Some examples of moment preserving approximation [ MR 1665362 ]
    • C. F. Bracciali — Relations between certain symmetric strong Stieltjes distributions [ MR 1665363 ]
    • Adhemar Bultheel, Carlos Díaz-Mendoza, Pablo González-Vera and Ramon Orive — Estimates of the rate of convergence for certain quadrature formulas on the half-line [ MR 1665364 ]
    • Adhemar Bultheel and Pablo González-Vera — Wavelets by orthogonal rational kernels [ MR 1665365 ]
    • Heng Huat Chan and Victor Tan — On the explicit evaluations of the Rogers-Ramanujan continued fraction [ MR 1665366 ]
    • Dov Chelst — Absence of phase transitions in modified two-component plasmas: the analytic theory of continued fractions in statistical mechanics [ MR 1665367 ]
    • Mourad E. H. Ismail and David R. Masson — Some continued fractions related to elliptic functions [ MR 1665368 ]
    • William B. Jones and Guoxiang Shen — Asymptotics of Stieltjes continued fraction coefficients and applications to Whittaker functions [ MR 1665369 ]
    • L. J. Lange — A generalization of Van Vleck’s theorem and more on complex continued fractions [ MR 1665370 ]
    • Xin Li — Convergence of interpolating Laurent polynomials on an annulus [ MR 1665371 ]
    • Lisa Lorentzen — Convergence criteria for continued fractions $K(a_n/1)$ based on value sets [ MR 1665372 ]
    • Olav Njåstad — Strong Stieltjes moment problems [ MR 1665373 ]
    • Franz Peherstorfer and Robert Steinbauer — Weak asymptotics of orthogonal polynomials on the support of the measure of orthogonality and considerations on functions of the second kind [ MR 1665374 ]
    • Serge Perrine — Trees of approximation constants [ MR 1665375 ]
    • Igor Rodnianski — Continued fractions and Schrödinger evolution [ MR 1665376 ]
    • Walter Van Assche — Multiple orthogonal polynomials, irrationality and transcendence [ MR 1665377 ]
    • Alfred J. van der Poorten — Reduction of continued fractions of formal power series [ MR 1665378 ]
    • Haakon Waadeland — Some observations in frequency analysis [ MR 1665379 ]
    • Franck Wielonsky — Some properties of Hermite-Padé approximants to $e^z$ [ MR 1665380 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2361999; 379 pp
MSC: Primary 42; 30; 40; Secondary 11; 33; 41

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.

  • Articles
  • Richard Askey — Continued fractions and orthogonal polynomials [ MR 1665360 ]
  • Bruce C. Berndt, Youn-Seo Choi and Soon-Yi Kang — The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society [ MR 1665361 ]
  • B. Bojanov and A. Sri Ranga — Some examples of moment preserving approximation [ MR 1665362 ]
  • C. F. Bracciali — Relations between certain symmetric strong Stieltjes distributions [ MR 1665363 ]
  • Adhemar Bultheel, Carlos Díaz-Mendoza, Pablo González-Vera and Ramon Orive — Estimates of the rate of convergence for certain quadrature formulas on the half-line [ MR 1665364 ]
  • Adhemar Bultheel and Pablo González-Vera — Wavelets by orthogonal rational kernels [ MR 1665365 ]
  • Heng Huat Chan and Victor Tan — On the explicit evaluations of the Rogers-Ramanujan continued fraction [ MR 1665366 ]
  • Dov Chelst — Absence of phase transitions in modified two-component plasmas: the analytic theory of continued fractions in statistical mechanics [ MR 1665367 ]
  • Mourad E. H. Ismail and David R. Masson — Some continued fractions related to elliptic functions [ MR 1665368 ]
  • William B. Jones and Guoxiang Shen — Asymptotics of Stieltjes continued fraction coefficients and applications to Whittaker functions [ MR 1665369 ]
  • L. J. Lange — A generalization of Van Vleck’s theorem and more on complex continued fractions [ MR 1665370 ]
  • Xin Li — Convergence of interpolating Laurent polynomials on an annulus [ MR 1665371 ]
  • Lisa Lorentzen — Convergence criteria for continued fractions $K(a_n/1)$ based on value sets [ MR 1665372 ]
  • Olav Njåstad — Strong Stieltjes moment problems [ MR 1665373 ]
  • Franz Peherstorfer and Robert Steinbauer — Weak asymptotics of orthogonal polynomials on the support of the measure of orthogonality and considerations on functions of the second kind [ MR 1665374 ]
  • Serge Perrine — Trees of approximation constants [ MR 1665375 ]
  • Igor Rodnianski — Continued fractions and Schrödinger evolution [ MR 1665376 ]
  • Walter Van Assche — Multiple orthogonal polynomials, irrationality and transcendence [ MR 1665377 ]
  • Alfred J. van der Poorten — Reduction of continued fractions of formal power series [ MR 1665378 ]
  • Haakon Waadeland — Some observations in frequency analysis [ MR 1665379 ]
  • Franck Wielonsky — Some properties of Hermite-Padé approximants to $e^z$ [ MR 1665380 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.