Handbook of Continued Fractions for Special Functions

• Main Authors: Cuyt, Annie (Author), Petersen, Vigdis Brevik (Author), Verdonk, Brigitte (Author), Waadeland, Haakon (Author), Jones, William B. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands, 2008.
• Subjects: Mathematics.; Science.; Computer science > Mathematics.; Special functions.; Engineering.; Applied mathematics.; Engineering mathematics.; Special Functions.; Appl.Mathematics/Computational Methods of Engineering.; Mathematics, general.; Mathematics of Computing.; Engineering, general.; Science, general.

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 col...

Table of Contents:

• Basic Theory
• Basics
• Continued fraction representation of functions
• Convergence criteria
• Padé approximants
• Moment theory and orthogonal functions
• Numerics
• Continued fraction construction
• Truncation error bounds
• Continued fraction evaluation
• Special Functions
• On tables and graphs
• Mathematical constants
• Elementary functions
• Gamma function and related functions
• Error function and related integrals
• Exponential integrals and related functions
• Hypergeometric functions
• Confluent hypergeometric functions
• Bessel functions
• Probability functions
• Basic hypergeometric functions.