A Course of Modern AnalysisCambridge University Press, 13 sept. 1996 - 608 pages 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. |
Table des matières
Complex Numbers | 3 |
The Theory of Convergence | 11 |
Continuous Functions and Uniform Convergence | 41 |
The Theory of Rieman Integration | 61 |
The fundamental properties of Analytic Functions Taylors Laurents and Liouvilles Theorems | 82 |
The Theory of Residues application to the evaluation of Definite Integrals | 111 |
The expansion of functions in Infinite Series | 125 |
Asymptotic Expansions and Summable Series | 150 |
The Hypergeometric Function | 281 |
Legendre Functions | 302 |
The Confluent Hypergeometric Function | 337 |
Bessel Functions | 355 |
The Equations of Mathematical Physics | 386 |
Mathieu Functions | 404 |
Elliptic Functions General theorems and the Weierstrassian Functions | 429 |
The Theta Functions | 462 |
Fourier Series and Trigonometrical Series | 160 |
Linear Differential Equations | 194 |
Integral Equations | 211 |
THE TRANSCENDENTAL FUNCTIONS | 233 |
The Gamma Function | 235 |
The Zeta Function of Rieman | 265 |
The Jacobian Elliptic Functions | 491 |
Ellipsoidal Harmonics and Lames Equation | 536 |
APPENDIX | 579 |
| 591 | |
| 595 | |
Autres éditions - Tout afficher
A Course of Modern Analysis: An Introduction to the General Theory of ... Edmund Taylor Whittaker,George Neville Watson Aucun aperçu disponible - 1940 |
Expressions et termes fréquents
a₁ absolutely convergent analytic function asymptotic expansion b₁ Bessel circle coefficients complex number constant continuous function contour convergent series converges absolutely converges uniformly Corollary cosh deduce defined denote differential equation doubly-periodic function ellipsoidal harmonics elliptic functions Example expression formula Fourier series given Hence hypergeometric independent infinite integer integral equation integrand Jacobi Jacobian elliptic functions Journal für Math Lamé functions Laplace's equation linear London Math Mathieu functions Mathieu's modulus multiplied notation obtained one-valued P₁ P₂ path of integration periodic points poles polynomial positive integer positive number Proc Prove real numbers residues result Riemann's satisfied series converges Shew shewn sin³ singularities sn² sn³ solution tends to zero theorem theory Theta-functions Trip values variable w₁ write