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Title Details:
Elements of asymptotic analysis
Other Titles: Integrals, sums, special functions
Authors: Doumas, Aristides
Reviewer: Konstandopoulos, Takis
Subject: MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > ORDINARY DIFFERENTIAL EQUATIONS > ASYMPTOTIC THEORY
Keywords:
Asymptotic expansion
Asymptotic series
Laplace integrlas
Watson's lemma
Method of steepest descents
Stokes phenomenon
Method of stationary phase
Asymptotic behaviour of sums
Euler Maclaurin summation formula
Special functions
Description:
Abstract:
This book serves the basic techniques in asymptotic analysis and is divided in two parts. The first part deals with the asymptotic behavior of integrals. We present the Laplace method for integrals, and Watson’s lemma. We continue with the method of steepest descents and the method of stationary phase. Emphasis has been given on some special functions, e.g., Gamma, Airy, Bessel. The second part studies the asymptotic behaviors of sums. The main tools are summation by parts, Euler Maclaurin summation formula, and Laplace method for sums
Linguistic Editors: Kalliaras, Dimitrios
Technical Editors: Karatzidis, Dimitrios
Graphic Editors: Douma, Emmeleia-Anastasia
Type: Undergraduate textbook
Creation Date: 2022
Item Details:
ISBN 978-618-85850-9-6
License: Attribution - NonCommercial - ShareAlike 4.0 International (CC BY-NC-SA 4.0)
DOI http://dx.doi.org/10.57713/kallipos-38
Handle http://hdl.handle.net/11419/8415
Bibliographic Reference: Doumas, A. (2022). Elements of asymptotic analysis [Undergraduate textbook]. Kallipos, Open Academic Editions. http://dx.doi.org/10.57713/kallipos-38
Language: Greek
Consists of:
1. Introduction
2. Asymptotic expansions of integrals
3. Asymptotic expansions of sums
Publication Origin: Kallipos, Open Academic Editions