| Contents Notes |
List of Computer Programs -- 1. Bernoulli and Euler Numbers -- 2. Orthogonal Polynomials -- 3. Gamma, Beta, and PSI Functions -- 4. Legendre Functions -- 5. Bessel Functions -- 6. Modified Bessel Functions -- 7. Integrals of Bessel Functions -- 8. Spherical Bessel Functions -- 9. Kelvin Functions -- 10. Airy Functions -- 11. Struve Functions -- 12. Hypergeometric and Confluent Hypergeometric Functions -- 13. Parabolic Cylinder Functions -- 14. Mathieu Functions -- 15. Spheroidal Wave Functions -- 16. Error Function and Fresnel Integrals -- 17. Cosine and Sine Integrals -- 18. Elliptic Integrals and Jacobian Elliptic Functions -- 19. Exponential Integrals -- 20. Summary of Methods for Computing Special Functions -- App. A. Derivation of Some Special Differential Equations -- App. B. Root-Finding Methods -- App. C. About the Software. Computation of Special Functions is a valuable book/software package containing more than 100 original computer programs for the computation of most special functions currently in use. These include many functions commonly omitted from available software packages, such as the Bessel and modified Bessel functions, the Mathieu and modified Mathieu functions, parabolic cylinder functions, and various prolate and oblate spheroidal wave functions. Also, unlike most software packages, this book/disk set gives readers the latitude to modify programs according to the special demands of the sophisticated problems they are working on. The authors provide detailed descriptions of the program's algorithms as well as specific information about each program's internal structure. |
