Abstract/Details

Algorithms for series coefficients


2001 2001

Other formats: Order a copy

Abstract (summary)

The expansion of Taylor series is a very old topic in both pure and applied mathematics. It plays a crucial role in fundamental theory and applications. Computer algebra systems provide an interactive environment to assist in solving many mathematical problems. This work focuses on the development of techniques and algorithms for determining the coefficients in the Taylor expansion of a function. Our goal is to provide a set of procedures that can be implemented with these systems.

In this work, by comparing coefficients and taking derivatives, we develop some new methods called exact methods. We introduce transform methods, which is based on Laplace transformation, and discuss asymptotic methods, which is based on Integration.

The algorithms we developed are capable of obtaining closed forms and asymptotic information for a much wider class of functions than is possible using current techniques and existing theories. Furthermore, we will be able to demonstrate the superiority of our methods by implementing them using the Maple computer algebra system and comparing the results with those obtained by others.

Indexing (details)


Subject
Mathematics;
Computer science;
Statistics
Classification
0405: Mathematics
0984: Computer science
0463: Statistics
Identifier / keyword
Applied sciences; Pure sciences; Exact methods; Series coefficients; Taylor series; Transform methods
Title
Algorithms for series coefficients
Author
Zhang, Jun
Number of pages
66
Publication year
2001
Degree date
2001
School code
0186
Source
DAI-B 63/01, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780493525068, 0493525068
Advisor
Lamagna, Ed
University/institution
University of Rhode Island
University location
United States -- Rhode Island
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3039089
ProQuest document ID
304725291
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304725291
Access the complete full text

You can get the full text of this document if it is part of your institution's ProQuest subscription.

Try one of the following:

  • Connect to ProQuest through your library network and search for the document from there.
  • Request the document from your library.
  • Go to the ProQuest login page and enter a ProQuest or My Research username / password.