Infinite sequences and series

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Infinite sequences and series / by Konrad Knopp ; translated by Frederick Bagemihl

資料種別:

図書

出版情報:

New York : Dover Publications, c1956

形態:

v, 186 p. ; 21 cm

著者名:

ISBN:

9780486601533 [0486601536]

書誌ID:

BA07554616

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Bibliography: p. 175-176
Includes index

主題:

Processes, Infinite; Series, Infinite

言語:

英語

目次情報:

Foreword

Introduction and Prerequisites / Chapter 1：

Preliminary remarks concerning sequences and series / 1.1：

Real and complex numbers / 1.2：

Sets of numbers / 1.3：

Functions of a real and of a complex variable / 1.4：

Sequences and Series / Chapter 2：

Arbitrary sequences / 2.1：

Null sequences

Sequences and sets of numbers / 2.2：

Convergence and divergence / 2.3：

Cauchy's limit theorem and its generalizations / 2.4：

The main tests for sequences / 2.5：

Infinite series / 2.6：

The Main Tests for Infinite Series / Chapter 3：

Operating with Convergent Series

Series of positive terms: The first main test and the comparison tests of the first and second kind / 3.1：

The radical test and the ratio test / 3.2：

Series of positive, monotonically decreasing terms / 3.3：

The second main test / 3.4：

Absolute convergence / 3.5：

Operating with convergent series / 3.6：

Infinite products / 3.7：

Power Series / Chapter 4：

The circle of convergence / 4.1：

The functions represented by power series / 4.2：

Operating with power series / 4.3：

Expansion of composite functions

The inversion of a power series / 4.4：

Development of the Theory of Convergence / Chapter 5：

The theorems of Abel, Dini, and Pringsheim / 5.1：

Scales of convergence tests / 5.2：

Abel's partial summation / 5.3：

Lemmas

Special comparison tests of the second kind / 5.4：

Abel's and Dirichlet's tests and their generalizations / 5.5：

Series transformations / 5.6：

Multiplication of series / 5.7：

Expansion of the Elementary Functions / Chapter 6：

List of the elementary functions / 6.1：

The rational functions / 6.2：

The exponential function and the circular functions / 6.3：

The logarithmic function / 6.4：

The general power and the binomial series / 6.5：

The cyclometric functions / 6.6：

Numerical and Closed Evaluation of Series / Chapter 7：

Statement of the problem / 7.1：

Numerical evaluations and estimations of remainders / 7.2：

Closed evaluations Bibliography / 7.3：

Index

Foreword

Introduction and Prerequisites / Chapter 1：

Preliminary remarks concerning sequences and series / 1.1：

Real and complex numbers / 1.2：

Sets of numbers / 1.3：

Functions of a real and of a complex variable / 1.4：

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