| Author |
Fikioris, George J., 1962-
|
| Title |
Mellin-transform method for integral evaluation / George Fikioris. |
| Edition |
First edition. |
| OCLC |
200612CEM013 |
| ISBN |
1598291858 (electronic bk.) |
|
9781598291858 (electronic bk.) |
|
159829184X (pbk.) |
|
9781598291841 (pbk.) |
| ISBN/ISSN |
10.2200/S00076ED1V01Y200612CEM013 doi |
| Publisher |
San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, [2007] |
|
©2007 |
| Description |
1 electronic text (ix, 67 pages : illustrations\.) : digital file. |
| LC Subject heading/s |
Antennas (Electronics) -- Mathematical models.
|
|
Mellin transform.
|
| SUBJECT |
Integration (Mathematics)
|
|
Mellin transforms.
|
|
Antenna theory.
|
|
Electromagnetic theory.
|
| System details note |
Mode of access: World Wide Web. |
|
System requirements: Adobe Acrobat Reader. |
| Bibliography |
Includes bibliographical references (pages 61-65). |
| 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. |
| Restrictions |
Abstract freely available; full-text restricted to subscribers or individual document purchasers. |
|
Access may be restricted to authorized users only. |
|
Unlimited user license access |
| NOTE |
Compendex. |
|
INSPEC. |
|
Google book search. |
| Summary |
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 yielding closed-form expressions very difficult to come up with other methods or to deduce from the usual tables of integrals. Yet, as opposed to other methods, the present method is very straightforward to apply; it usually requires laborious calculations, but little ingenuity. Two functions, the generalized hypergeometric function and the Meijer G-function, are very much related to the Mellin-transform method and arise frequently when the method is applied. Because these functions can be automatically handled by modern numerical routines, they are now much more useful than they were in the past. |
| NOTE |
Google scholar. |
| Additional physical form available note |
Also available in print. |
| General note |
Part of: Synthesis digital library of engineering and computer science. |
|
Title from PDF t.p. (viewed Oct. 19, 2008). |
|
Series from website. |
|
