An Introduction to the Theory of Infinite Series

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American Mathematical Soc., 2005 - Mathematics - 535 pages
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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.
 

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Contents

CHAPTER I
1
CHAPTER II
26
CHAPTER III
53
CHAPTER IV
69
Double Series 7897
78
CHAPTER VI
104
Examples
114
CHAPTER VIII
145
CHAPTER XI
278
CHAPTER XII
317
Asymptotic Series 324354
324
Trigonometrical Series 354387
354
APPENDIX I
394
Examples
430
APPENDIX II
436
Some Theorems on Infinite Integrals and Gamma
461

Special Power Series 170189
170
CHAPTER IX
202
CHAPTER X
227
Examples
267
Examples
514
MISCELLANEOUS EXAMPLES
526
GENERAL INDEX 533535
533
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