## A Course of Modern AnalysisThis 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. |

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### Contents

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 | |

### Other editions - View all

A Course of Modern Analysis: An Introduction to the General Theory of ... Edmund Taylor Whittaker No preview available - 2013 |

### Common terms and phrases

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