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Series play a decisive role in many branches of mathematics. They accompanied mathematical developments from Zeno of Elea (##5##-th century BC) and Archimedes of Syracuse (##3##-th century BC), to the fundamental building blocks of calculus from the ##17##-th century on, up to modern Lie theory which is crucial for our understanding of quantum theory. Series are probably the second most important objects in mathematics after functions. And the latter have often been expressed by series, especially in analysis. The termanalytical functionorholomorphic functionrepresents such an identification.

A series itself is just an expression ...

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