Synopses & Reviews
This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever.
The classic text on mathematical analysis.
This classic text is known to and used by thousands of mathematicians and students of mathematics thorughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principle transcendental functions.
Table of Contents
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; 6. The theory of residues; 7. The expansion of functions in infinite series; 8. Asymptotic expansions and summable series; 9. Fourier series and trigonometrical series; 10. Linear differential equations; 11. Integral equations; 12. The gamma function; 13. The zeta function of Riemann; 14. The hypergeometric function; 15. The Legendre function; 16. The confluent hypergeometric functions; 17. Bessel functions; 18. The equations of mathematical physics; 19. Mathieu functions; 20. Elliptic functions; 21. The theta functions; 22. Jacobian elliptic functions; 23. Ellipsoidal harmonics and Lamé's equation.