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Advanced Mathematics for Applications by Andrea Prosperetti

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8

Sequences and Series

The solution of many of the problems considered in Part I of this book takes the form of an infinite series. We have made occasional statements about the convergence properties of these series in connection with specific results. Here we begin to address in greater detail and in more general terms this issue, which is of fundamental importance for these and many other applications.

We start from the simplest case, numerical sequences and series, and we then proceed to consider sequences and series of functions. We conclude with some practical methods to generate closed-form expressions for the sum of an infinite series.

While some of the concepts introduced in this chapter may appear straightforward, their real ...

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