Mellin-transform method for integral evaluation

Fikioris, G

dc.contributor.author	Fikioris, G	en
dc.date.accessioned	2014-03-01T01:26:36Z
dc.date.available	2014-03-01T01:26:36Z
dc.date.issued	2007	en
dc.identifier.issn	19321252	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18154
dc.subject	Antenna Theory	en
dc.subject	Electromagnetic Theory	en
dc.subject	Integration (Mathematics)	en
dc.subject	Mellin Transforms	en
dc.subject.other	Electromagnetism	en
dc.subject.other	Function evaluation	en
dc.subject.other	Integration	en
dc.subject.other	Mathematical transformations	en
dc.subject.other	Numerical methods	en
dc.subject.other	Problem solving	en
dc.subject.other	Antenna Theory	en
dc.subject.other	Electromagnetic Theory	en
dc.subject.other	Mellin Transforms	en
dc.subject.other	Integral equations	en
dc.title	Mellin-transform method for integral evaluation	en
heal.type	journalArticle	en
heal.identifier.primary	10.2200/S00076ED1V01Y200612CEM013	en
heal.identifier.secondary	http://dx.doi.org/10.2200/S00076ED1V01Y200612CEM013	en
heal.publicationDate	2007	en
heal.abstract	This book introduces the Mellin-transform method for the exact calculation of one-dimensional definite integrals and illustrates the application of 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 using other methods or to deduce from the usual tables of integrals. Yet, as opposed to those that require laborious calculations with little ingenuity, the present method is very straightforward to apply. Two functions, the generalized hyper-geometric 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. The Mellin-transform method and the two aforementioned functions are discussed first. Then the method is applied in three examples to obtain results, which, at least in the antenna/electromagnetics literature, are believed to be new. In the first example, a closed-form expression, as a generalized hyper-geometric function, is obtained for the power radiated by a constant-current circular-loop antenna. The second example concerns the admittance of a 2-D slot antenna. In both these examples, the exact closed-form expressions are applied to improve upon existing formulas in standard antenna textbooks. In the third example, a very simple expression for an integral arising in recent, unpublished studies of unbounded, biaxially an isotropic media is derived. Additional examples are also briefly discussed. © Copyright 2007 by Morgan & Claypool 2007.	en
heal.journalName	Synthesis Lectures on Computational Electromagnetics	en
dc.identifier.doi	10.2200/S00076ED1V01Y200612CEM013	en
dc.identifier.volume	13	en
dc.identifier.spage	1	en
dc.identifier.epage	67	en