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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.

## 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.

## Subfields

• 40A: Convergence and divergence of infinite limiting processes
• 40B05: Multiple sequences and series (should also be assigned at least one other classification number in this section)
• 40C: General summability methods
• 40D: Direct theorems on summability
• 40E: Inversion theorems
• 40F05: Absolute and strong summability
• 40G: Special methods of summability
• 40H05: Functional analytic methods in summability

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

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