Mellin-transform method for integral evaluation

• Main Author: Fikioris, George J., 1962-
• Format: Electronic
• Language: English
• Published: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2007.
• Edition: 1st ed.
• Series: Synthesis lectures on computational electromagnetics (Online), #13.
• Subjects: Antennas (Electronics) > Mathematical models.; Mellin transform.
• Online Access: Abstract with links to full text

This book introduces the Mellin-transform method for the exact calculation of one-dimensional definite integrals, and illustrates the application if this method to electromagnetics problems. Once the basics have been mastered, one quickly realizes that the method is extremely powerful, often yieldin...

Table of Contents:

• Preface
• 1. Introduction
• 2. Mellin transforms and the gamma function
• 2.1. Mellin transform : definition, strip of analyticity (SOA)
• 2.2. Mellin transform : basic properties
• 2.3. Mellin transform : Parseval formula and related properties
• 2.4. Gamma function
• 2.5. Psi function
• 2.6. Pochhammer's symbol
• 2.7. Simple applications
• 2.8. Table lookup of Mellin transforms : Mellin-Barnes integrals
• 3. Generalized hypergeometric functions, Meijer g-functions, and their numerical computation
• 3.1. Definitions
• 3.2. Remarks
• 3.3. Numerical computation of p Fq and G
• 4. The Mellin-transform method of evaluating integrals
• 4.1. A general description of the Mellin-transform method
• 4.2. A first example
• 5. Power radiated by certain circular antennas
• 5.1. Constant-current circular-loop antennas
• 5.2. Circular-patch microstrip antennas : Cavity model
• 5.3. Integral evaluation
• 5.4. Application to electrically large loop antennas
• 6. Aperture admittance of a 2-D slot antenna
• 7. An integral arising in the theory of biaxially anisotropic media
• 8. On closing the contour
• 9. Further discussions
• 9.1. A note regarding Mellin convolution
• 9.2. On the use of symbolic routines
• 9.3. Complex values of the parameter x
• 9.4. Significance of the poles to the right : asymptotic expansions
• 9.5. Relations of our results to entries in integral tables
• 9.6. Numerical evaluation of integrals by modern routines
• 9.7. Additional reading
• 10. Summary and conclusions
• Appendix A. On the convergence/divergence of definite integrals
• A. 1. Some remarks on our rules
• A. 2. Rules for determining convergence/divergence
• A. 3. Examples
• Appendix B. The lemma of section 2.7
• B. 1. Preliminary identities
• B. 2. Derivation of (2.38)
• Appendix C. Alternative derivations or verifications for the integrals of section 4.2, and chapters 5 and 6
• Appendix D. Additional examples from the electromagnetics area
• D. 1. An integral arising in a rain attenuation problem
• D. 2. An integral relevant to the thin-wire loop antenna
• References
• Author biography.