Multiple series

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$ s $- tuple series

An expression of the form

$$ \sum _ {m,n \dots p = 1 } ^ \infty u _ {m, n \dots p } , $$

consisting of the terms from a table $ \| u _ {m, n \dots p } \| $. Each term of the table is indexed by $ s \geq 2 $ indices $ m, n \dots p $, which run independently of each other over the set of natural numbers. The theory of multiple series is analogous to the theory of double series. See also Absolutely convergent series.


[1] G.M. Fichtenholz, "Differential und Integralrechnung" , 2 , Deutsch. Verlag Wissenschaft. (1964)
How to Cite This Entry:
Multiple series. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by E.G. Sobolevskaya (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article