Integral evaluation using the mellin transform and generalized hypergeometric functions: Tutorial and applications to antenna problems

Fikioris, G

dc.contributor.author	Fikioris, G	en
dc.date.accessioned	2014-03-01T11:44:42Z
dc.date.available	2014-03-01T11:44:42Z
dc.date.issued	2006	en
dc.identifier.issn	0018-926X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/37108
dc.subject	Antenna theory	en
dc.subject	Integration (mathematics)	en
dc.subject	Mellin transforms	en
dc.subject.classification	Engineering, Electrical & Electronic	en
dc.subject.classification	Telecommunications	en
dc.subject.other	Antenna area	en
dc.subject.other	Antenna theory	en
dc.subject.other	Closed-form expression	en
dc.subject.other	Constant-current	en
dc.subject.other	Definite integral	en
dc.subject.other	Exact calculations	en
dc.subject.other	First-principles	en
dc.subject.other	Generalized hypergeometric functions	en
dc.subject.other	Integral evaluation	en
dc.subject.other	Mathematica	en
dc.subject.other	Mellin transform	en
dc.subject.other	Mellin-Barnes integrals	en
dc.subject.other	Simple expression	en
dc.subject.other	Standard antenna	en
dc.subject.other	Step-by-step	en
dc.subject.other	Antenna arrays	en
dc.subject.other	Slot antennas	en
dc.subject.other	Wavelet transforms	en
dc.subject.other	Anisotropic media	en
dc.title	Integral evaluation using the mellin transform and generalized hypergeometric functions: Tutorial and applications to antenna problems	en
heal.type	other	en
heal.identifier.primary	10.1109/TAP.2006.886579	en
heal.identifier.secondary	http://dx.doi.org/10.1109/TAP.2006.886579	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	This is a tutorial presentation of the Mellin-transform (MT) method for the exact calculation of one-dimensional definite integrals, and an illustration of the application of this method to antenna/electromagnetics problems. Once the basics have been mastered, one quickly realizes that the MT-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 MT-method is very straightforward to apply; it usually requires laborious calculations, but little ingenuity. In fact, the MT-method is used by Mathematica to symbolically calculate definite integrals. The first part of this paper is a step-by-step tutorial, proceeding from first principles. It includes basic information on Mellin-Barnes integrals and generalized hypergeometric functions, and summarizes the key ideas of the MT-method. In the remaining parts, the MT-method is applied to three examples from the antenna area. The results here are believed to be new, at least in the antenna/electromagnetics literature. In our first example, we obtain a closed-form expression, as a generalized hypergeometric function, for the power radiated by a constant-current circular-loop antenna; this quantity has been extensively discussed recently. Our 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 our third example, finally, we obtain a very simple expression for an integral arising in recent, unpublished studies of unbounded, biaxially anisotropic media. © 2006 IEEE.	en
heal.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC	en
heal.journalName	IEEE Transactions on Antennas and Propagation	en
dc.identifier.doi	10.1109/TAP.2006.886579	en
dc.identifier.isi	ISI:000242814800045	en
dc.identifier.volume	54	en
dc.identifier.issue	12	en
dc.identifier.spage	3895	en
dc.identifier.epage	3907	en