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Handbook of Continued Fractions for Special Functions

  • Annie Cuyt
  • Vigdis Brevik Petersen
  • Brigitte Verdonk
  • Haakon Waadeland
  • William B. Jones

Table of contents

  1. Front Matter
    Pages I-6
  2. Basic Theory

    1. Front Matter
      Pages 7-7
    2. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 9-28
    3. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 29-43
    4. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 45-58
    5. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 59-75
    6. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 77-104
  3. Numerics

    1. Front Matter
      Pages 105-105
    2. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 107-128
    3. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 129-147
    4. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 148-159
  4. Special Functions

    1. Front Matter
      Pages 161-161
    2. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 163-173
    3. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 175-191
    4. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 193-220
    5. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 221-251
    6. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 253-273
    7. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 275-290
    8. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 291-317
    9. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 319-341
    10. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 343-369
    11. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 371-389
    12. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 391-400
  5. Back Matter
    Pages 401-431

About this book

Introduction

Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, namely the Handbook of Mathematical Functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies!

But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!

Keywords

Hypergeometric function brandon wis chemistry computer computer science function gamma function numerics physics science statistics

Authors and affiliations

  • Annie Cuyt
    • 1
  • Vigdis Brevik Petersen
    • 2
  • Brigitte Verdonk
    • 1
  • Haakon Waadeland
    • 3
  • William B. Jones
    • 4
  1. 1.Department of Mathematics and Computer ScienceUniversity of AntwerpBelgium
  2. 2.Faculty of Teacher and Interpreter EducationSør-Trøndelag University CollegeNO-7004 TrondheimNorway
  3. 3.Department of Mathematical SciencesNorwegian University of Science and TechnologyNorway
  4. 4.Department of MathematicsUniversity of ColoradoBoulderUSA

Bibliographic information