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40: Sequences, series, summability


Introduction

Sequences and series are really just the most common examples of limiting processes; convergence criteria and rates of convergence are as important as finding "the answer". (In the case of sequences of functions, it's also important do find "the question"!) Particular series of interest (e.g. Taylor series of known functions) are of interest, as well as general methods for computing sums rapidly, or formally. Series can be estimated with integrals, their stability can be investigated with analysis. Manipulations of series (e.g. multiplying or inverting) are also of importance.

History

Applications and related fields

Sequences are discussed here, but for sequences of integers and their number-theoretic properties, see number theory.

Finite trigonometric sums are treated in 11L: Exponential sums and character sums.

The general question of whether or not a function defined by a series can be evaluated simply in terms of "known" functions is delicate; by analogy with differential equations, it is possible to deduce some answers using the tools of 12H: Differential and difference algebra [Schematic of subareas and related areas]

Subfields

This is one of the smallest areas in the Math Reviews database.

Browse all (old) classifications for this area at the AMS.


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Last modified 2000/01/17 by Dave Rusin. Mail: