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Definition: Convergent Complex Series
A complex series \(\sum_{k=0}^\infty x_k\) is called convergent, if the complex sequence \((s_n)_{n\in\mathbb N}\) of partial sums \[s_n:=\sum_{k=0}^n x_k,\quad\quad n\in\mathbb N\] is a convergent complex sequence.
For convergent complex series, the notation
\[\sum_{k=0}^\infty x_k\]
can, depending on the context, denote two things:
 the convergent real series itself or
 the convergent real series itself or
Table of Contents
 Proposition: A General Criterion for the Convergence of Infinite Complex Series
Mentioned in:
Definitions: 1
Proofs: 2
Propositions: 3
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer VerĂ¤nderlichen", Vieweg Studium, 1983