Analytic Theory of Continued Fractions (AMS Chelsea Publishing)

Publisher: American Mathematical Society
Number Of Pages: 433
Publication Date: 2000-01
Sales Rank: 1237861
ISBN / ASIN: 0821821067
EAN: 9780821821060
Binding: Hardcover
Manufacturer: American Mathematical Society
Studio: American Mathematical Society

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 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.

From the Preface (1948): "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 ... "

A Classic on The COntinued Fraction Theory, Hard to find in Libraries, AMS - CHELSEA publishing. dedicated to all gigapedians....