## Book description

This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include some recent, direct applications to antennas and computational electromagnetics. Then, specific methods are discussed. These include integration by parts and the Riemann-Lebesgue lemma, the use of contour integration in conjunction with other methods, techniques related to Laplace's method and Watson's lemma, the asymptotic behavior of certain Fourier sine and cosine transforms, and the Poisson summation formula (including its version for finite sums). Often underutilized in the literature are asymptotic techniques based on the Mellin transform; our treatment of this subject complements the techniques presented in our recent Synthesis Lecture on the exact (not asymptotic) evaluation of integrals.

1. Preface
2. Introduction: Simple Asymptotic Approximations
1. Far Field of Linear Antenna
2. Period of Simple Pendulum: Small Oscillations
3. A Differential Equation
4. Asymptotic Approximations for High-SWR Transmission Lines
5. Supplementary Remarks and Further Reading
6. Problems
7. References
3. Asymptotic Approximations Defined
1. Definitions
2. Remarks and Examples
3. Compound Asymptotic Approximations
4. Asymptotic Expansions
5. Historical and Supplementary Remarks
6. Problems
7. References
4. Concepts from Complex Variables
1. Gamma Function and Related Functions
2. Power Series
3. Analytic Continuation
4. Multivalued Functions and Branch Points
5. Branches and Principal Values of Multivalued Functions
6. Applications to Antennas and Electromagnetics: Nonsolvability
7. Supplementary Remarks and Further Reading
8. Problems (1/2)
9. Problems (2/2)
10. References
5. Laplace's Method and Watson's Lemma
1. Laplace's Method
2. Watson's Lemma
4. Problems
5. References
6. Integration by Parts and Asymptotics of Some Fourier Transforms
1. Integration by Parts and Laplace Transforms
2. Integration by Parts and Fourier Transforms
3. More on Fourier Transforms
4. Applications to Wire Antennas
5. Problems
6. References
7. Poisson Summation Formula and Applications
1. Doubly Infinite Sums
2. Finite Sums
3. Problems
4. References
8. Mellin-Transform Method for Asymptotic Evaluation of Integrals
9. More Applications to Wire Antennas
1. Problem Pertaining to Magnetic Frill Generator
2. Oscillations with the Approximate Kernel: Case of Delta-Function Generator
3. On the Near Field Due to Oscillating Current
4. Supplementary Remarks
5. Problems
6. References
10. Special Functions
1. Preliminaries
2. Exponential, Sine, and Cosine Integrals
3. Complete Elliptic Integral of the First Kind
4. Bessel and Hankel Functions
5. Modified Bessel Functions
6. Generalized Hypergeometric Functions
7. Problems
8. References
11. On the Convergence/Divergence of Definite Integrals
12. Authors' Biographies
13. Index (1/2)
14. Index (2/2)

## Product information

• Title: Selected Asymptotic Methods with Applications to Electromagnetics and Antennas
• Author(s): George Fikioris, Ioannis Tastsoglou, Odysseas N. Bakas
• Release date: September 2013
• Publisher(s): Morgan & Claypool Publishers
• ISBN: 9781627050401