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Analytic Theory of Continued Fractions
 
Analytic Theory of Continued Fractions
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-8218-2106-0
Product Code:  CHEL/207.H
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
Analytic Theory of Continued Fractions
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Analytic Theory of Continued Fractions
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-8218-2106-0
Product Code:  CHEL/207.H
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 2071948; 433 pp
    MSC: Primary 30; Secondary 40; 11;

    The theory of continued fractions has been defined by a small handful of books. This is one of them. The focus of Wall's book is on the study of continued fractions in the theory of analytic functions, rather than on arithmetical aspects. There are extended discussions of orthogonal polynomials, power series, infinite matrices and quadratic forms in infinitely many variables, definite integrals, the moment problem and the summation of divergent series.

    "In writing this book, I have tried to keep in mind the student of rather modest mathematical preparation, presupposing only a first course in function theory. Thus, I have included such things as a proof of Schwarz's inequality, theorems on uniformly bounded families of analytic functions, properties of Stieltjes integrals, and an introduction to the matrix calculus. I have presupposed a knowledge of the elementary properties of linear fractional transformations in the complex plane.

    It has not been my intention to write a complete treatise on the subject of continued fractions, covering all the literature, but rather to present a unified theory correlating certain parts and applications of the subject within a larger analytic structure ..."

    from the Preface

    Readership

    Graduate students and research mathematicians.

  • 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: 2071948; 433 pp
MSC: Primary 30; Secondary 40; 11;

The theory of continued fractions has been defined by a small handful of books. This is one of them. The focus of Wall's book is on the study of continued fractions in the theory of analytic functions, rather than on arithmetical aspects. There are extended discussions of orthogonal polynomials, power series, infinite matrices and quadratic forms in infinitely many variables, definite integrals, the moment problem and the summation of divergent series.

"In writing this book, I have tried to keep in mind the student of rather modest mathematical preparation, presupposing only a first course in function theory. Thus, I have included such things as a proof of Schwarz's inequality, theorems on uniformly bounded families of analytic functions, properties of Stieltjes integrals, and an introduction to the matrix calculus. I have presupposed a knowledge of the elementary properties of linear fractional transformations in the complex plane.

It has not been my intention to write a complete treatise on the subject of continued fractions, covering all the literature, but rather to present a unified theory correlating certain parts and applications of the subject within a larger analytic structure ..."

from the Preface

Readership

Graduate students and research mathematicians.

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
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