General considerations -- Part 1, Basic Theory -- 1. Basics -- 2. Continued fraction representation of functions -- 3. Convergence criteria -- 4. Pade approximants -- 5. Moment theory and orthogonal functions -- Part 2, Numerics -- 6. Continued fraction construction -- 7. Truncation error bounds -- 8. Continued fraction evaluation -- Part 3, Special Functions -- 9. On tables and graphs -- 10. Mathematical constants -- 11. Elementary functions -- 12. Gamma function and related functions -- 13. Error function and related integrals -- 14. Exponential integrals and related functions -- 15. Hypergeometric functions -- 16. Confluent hypergeometric functions, -- 17. Bessel functions -- 18. Probability functions -- 19. Basic hypergeometric functions .

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!