Ebook: Handbook of Continued Fractions for Special 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!

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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!

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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!

Content:
Front Matter....Pages I-6
Front Matter....Pages 7-7
Basics....Pages 9-28
Continued fraction representation of functions....Pages 29-43
Convergence criteria....Pages 45-58
Pad? approximants....Pages 59-75
Moment theory and orthogonal functions....Pages 77-104
Front Matter....Pages 105-105
Continued fraction construction....Pages 107-128
Truncation error bounds....Pages 129-147
Continued fraction evaluation....Pages 148-159
Front Matter....Pages 161-161
On tables and graphs....Pages 163-173
Mathematical constants....Pages 175-191
Elementary functions....Pages 193-220
Gamma function and related functions....Pages 221-251
Error function and related integrals....Pages 253-273
Exponential integrals and related functions....Pages 275-290
Hypergeometric functions....Pages 291-317
Confluent hypergeometric functions....Pages 319-341
Bessel functions....Pages 343-369
Probability functions....Pages 371-389
Basic hypergeometric functions....Pages 391-400
Back Matter....Pages 401-431

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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!

Content:
Front Matter....Pages I-6
Front Matter....Pages 7-7
Basics....Pages 9-28
Continued fraction representation of functions....Pages 29-43
Convergence criteria....Pages 45-58
Pad? approximants....Pages 59-75
Moment theory and orthogonal functions....Pages 77-104
Front Matter....Pages 105-105
Continued fraction construction....Pages 107-128
Truncation error bounds....Pages 129-147
Continued fraction evaluation....Pages 148-159
Front Matter....Pages 161-161
On tables and graphs....Pages 163-173
Mathematical constants....Pages 175-191
Elementary functions....Pages 193-220
Gamma function and related functions....Pages 221-251
Error function and related integrals....Pages 253-273
Exponential integrals and related functions....Pages 275-290
Hypergeometric functions....Pages 291-317
Confluent hypergeometric functions....Pages 319-341
Bessel functions....Pages 343-369
Probability functions....Pages 371-389
Basic hypergeometric functions....Pages 391-400
Back Matter....Pages 401-431
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