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Definition: Absolutely Convergent Complex Series

A complex series \(\sum_{k=0}^\infty x_k\) is a absolutely convergent complex series, if the series of absolute values of the summands \[\sum_{k=0}^\infty |x_k|\] is a convergent complex series.

Table of Contents

1. Proposition: Direct Comparison Test For Absolutely Convergent Complex Series
2. Proposition: Ratio Test For Absolutely Convergent Complex Series
3. Proposition: Cauchy Product of Absolutely Convergent Complex Series

Mentioned in:

Proofs: 1 2 3 4 5
Propositions: 6 7 8 9

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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983