Introduction to the Theory of Infinite Series

• 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.

“The book is especially good at counterexamples, and includes many of these to warn against pitfalls in reasoning and to show that all the hypotheses of the theorems are really needed. One especially nice feature is the use of Tannery’s theorem, on interchanging limit and summation, throughout the book.”-- MAA