Mathematics / Advanced, Mathematics / General, Mathematics / Probability & Statistics / General, Series, Infinite
Contents
Chapter 1. Operations on Series
1. Associativity of Convergent Series
2. Commutativity of Absolutely Convergent Series
3. Riemann's Theorem
4. Multiplication of Series
5. Toeplitz's Theorem
6. The Theorems of Mertens and Abel
Chapter 2. Iterated and Double Series
7. Iterated Series
8. Double Series
9. Examples
10. Power Series in Two Variables
Chapter 3. Computations Involving Series
11. General Remarks
12. Examples
13. Euler's Transformation
14. The Transformations of Kummer and Markov
Chapter 4. Summation of Divergel/t Series
15. Introduction
16. The Method of Power Series
17. The Method of Arithmetic Means
18. Application of Generalized Summation to Multiplication of Series
19. Other Methods of Generalized Summation
20. The Methods of Borel and Euler