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of series, sequences, integrals

The calculation of, respectively, the sums of series, the limits of sequences, and the values of integrals. The term "summation" also signifies the actual definition of the sum of a series (limit of a sequence, value of an integral), where in the usual definition these values do not exist, i.e. the series (sequence, integral) diverges. Such a definition is usually given in the form of a rule, and is called a summation method of series (sequences, integrals), cf. Summation methods.

How to Cite This Entry:
Summation. I.I. Volkov (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098