Whittaker, E. T., Watson, G.N. 　著

著者紹介

内容

目次

Introduction S. J. Patterson Part I. The Process of Analysis: 1. Complex numbers 2. The theory of convergence 3. Continuous functions and uniform convergence 4. The theory of Riemann integration 5. The fundamental properties of analytic functions – Taylor's, Laurent's and Liouville's theorems 6. The theory of residues – application to the evaluation of definite integrals 7. The expansion of functions in infinite series 8. Asymptotic expansions and summable series 9. Fourier series and trigonometric series 10. Linear differential equations 11. Integral equations Part II. The Transcendental Functions: 12. The Gamma-function 13. The zeta-function of Riemann 14. The hypergeometric function 15. Legendre functions 16. The confluent hypergeometric function 17. Bessel functions 18. The equations of mathematical physics 19. Mathieu functions 20. Elliptic functions. General theorems and the Weierstrassian functions 21. The theta-functions 22. The Jacobian elliptic functions 23. Ellipsoidal harmonics and Lamé's equation Appendix. The elementary transcendental functions References Author index Subject index.