An introduction to the theory of infinite series
著者
書誌事項
An introduction to the theory of infinite series
AMS Chelsea Publishing, 2002
3rd ed.
- : pbk
- タイトル別名
-
Infinite series
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注記
Reprint. Originally published: New York : Chelsea Publishing, 1991
Spine title: Infinite series
Includes bibliographical references and indexes
内容説明・目次
内容説明
This edition consists largely of a reproduction of the first edition (which was based on lectures on Elementary Analysis given at Queen's College, Galway, from 1902-1907), with additional theorems and examples. Additional material includes a discussion of the solution of linear differential equations of the second order; a discussion of elliptic function formulae; expanded treatment of asymptomatic series; a discussion of trigonometrical series, including Stokes's transformation and Gibbs's phenomenon; and an expanded Appendix II that includes an account of Napier's invention of logarithms.
目次
- Sequences and limits
- Series of positive terms
- Series in general
- Absolute convergence
- Double series
- Infinite products
- Series of variable terms
- Power series
- Special power series
- Trigonometrical formulae
- Complex series and products
- Special complex series and functions
- Non-convergent series
- Asymptotic series
- Trigonometrical series
- Appendix I. Arithmetic theory of irrational numbers and limits
- Appendix II. Definitions of the logarithmic and exponential functions
- Appendix III. Some theorems on infinite integrals and gamma-functions
- Miscellaneous examples
- Index of special integrals, products, and series
- General index
- Sequences and limits
- Series of positive terms
- Series in general
- Absolute convergence
- Double series
- Infinite products
- Series of variable terms
- Power series
- Special power series
- Trigonometrical formulae
- Complex series and products
- Special complex series and functions
- Non-convergent series
- Asymptotic series
- Trigonometrical series
- Appendix I. Arithmetic theory of irrational numbers and limits
- Appendix II. Definitions of the logarithmic and exponential functions
- Appendix III. Some theorems on infinite integrals and gamma-functions
- Miscellaneous examples
- Index of special integrals, products, and series
- General index
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