title: Neverending Fractions: An Introduction To Continued Fractions (Australian Mathematical Society Lecture Series)
author: Jonathan Borwein
description: This contemporary introduction to the fascinating theory of continued fractions covers a variety of applications that will interest graduates, postgraduates and researchers, as well as teachers and even amateur enthusiasts.
zlib_text: V 
  CONTINUED FRACTIONS AND THEIR APPLICATION 
  IN THE COMPUTATION OF DEFINITE 
  RIEMANN INTEGRALS 
  by 
  STANLEY MAX COMPTON, B.S. 
  A THESIS 
  IN 
  MATHEMATICS 
  Submitted to the Graduate Faculty 
  of Texas Tech University in 
  Partial Fulfillment of 
  the Requirements for 
  the Degree of 
  MASTER OF SCIENCE 
  Approved 
  August, 1973 
  
  ^ 
  ^^- 
  ^J 
  1973 
  ACKNOWLEDGMENTS 
  I would like to express my sincere appreciation to 
  Professor Vadim Komkov for his guidance with respect to 
  the development of this thesis, and to Professors 
  Charles N. Kellogg and Robert A. Moreland for their 
  helpful criticisms. I would also like to thank Mr. Joel R, 
  Wilson for his inspirational interest in this paper, and 
  Mrs. Anna F. Kirk for her fine editing and typing. 
  11 
  
  CONTENTS 
  ACK^^OWLEDGMENTS 
  ii 
  LIST OF TABLES 
  iv 
  I. INTRODUCTION AND HISTORICAL DEVELOPMENT . . . . . 
  1 
  Introduction 
  1 
  Historical Development 
  2 
  II. INTRODUCTORY CONCEPTS 
  6 
  Definitions and Notation 
  6 
  Successive Convergents 
  7 
  Convergence 
  1