Asymptotic Expansions

The Asymptotic Ring

The asymptotic ring, as well as its main documentation is contained in the module

• Asymptotic Ring.

Asymptotic Expansion Generators

Some common asymptotic expansions can be generated in

• Common Asymptotic Expansions.

Supplements

Behind the scenes of working with asymptotic expressions a couple of additional classes and tools turn up. For instance the growth of each summand is managed in growth groups, see below.

Growth Groups

The growth of a summand of an asymptotic expression is managed in

• (Asymptotic) Growth Groups and

• Cartesian Products of Growth Groups.

Term Monoids

A summand of an asymptotic expression is basically a term out of the following monoid:

• (Asymptotic) Term Monoids.

Miscellaneous

Various useful functions and tools are collected in

• Asymptotic Expansions — Miscellaneous.

Asymptotic Expansions — Table of Contents

• Asymptotic Ring
  • (Informal) Definition
    • Growth Groups and Elements
  • Introductory Examples
    • Two Rings
      • A Univariate Asymptotic Ring
      • A Multivariate Asymptotic Ring
    • Arithmetical Operations
      • The Ring Operations Plus and Times
      • Division
      • Powers, Expontials and Logarithms
      • Multivariate Arithmetic
  • More Examples
    • The mathematical constant e as a limit
  • Selected Technical Details
    • Coercions and Functorial Constructions
    • Data Structures
  • Various
  • Classes and Methods
• Common Asymptotic Expansions
  • Classes and Methods
• (Asymptotic) Growth Groups
  • Description of Growth Groups
  • Creating a Growth Group
    • Some Examples
  • Classes and Methods
• Cartesian Products of Growth Groups
  • Classes and Methods
• (Asymptotic) Term Monoids
  • Absorption of Asymptotic Terms
  • Comparison
  • Various
  • Classes and Methods
• Asymptotic Expansions — Miscellaneous
  • Functions, Classes and Methods
• Asymptotics of Multivariate Generating Series
  • Introductory Examples
  • Various
  • Classes and Methods

Indices and Tables

• Index

• Module Index

• Search Page