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020 _a9783031016974
_9978-3-031-01697-4
024 7 _a10.1007/978-3-031-01697-4
_2doi
050 4 _aT1-995
072 7 _aTBC
_2bicssc
072 7 _aTEC000000
_2bisacsh
072 7 _aTBC
_2thema
082 0 4 _a620
_223
100 1 _aFikioris, George.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_985283
245 1 0 _aMellin-Transform Method for Integral Evaluation
_h[electronic resource] :
_bIntroduction and Applications to Electromagnetics /
_cby George Fikioris.
250 _a1st ed. 2007.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2007.
300 _aIX, 67 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSynthesis Lectures on Computational Electromagnetics,
_x1932-1716
505 0 _aIntroduction -- Mellin Transforms and theGamma Function -- Generalized Hypergeometric Functions, Meijer G-Functions, and Their Numerical Computation -- The Mellin-Transform Method of Evaluating Integrals -- Power Radiated by Certain Circular Antennas -- Aperture Admittance of a 2-D Slot Antenna -- An Integral Arising in the Theory of Biaxially Anisotropic Media -- On Closing the Contour -- Further Discussions -- Summary and Conclusions.
520 _aThis 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. The Mellin-transform method and the two aforementioned functions are discussed first. Then the methodis 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 hypergeometric 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 anisotropic media is derived. Additional examples are also briefly discussed.
650 0 _aEngineering.
_99405
650 0 _aElectrical engineering.
_985284
650 0 _aTelecommunication.
_910437
650 1 4 _aTechnology and Engineering.
_985287
650 2 4 _aElectrical and Electronic Engineering.
_985288
650 2 4 _aMicrowaves, RF Engineering and Optical Communications.
_931630
710 2 _aSpringerLink (Online service)
_985291
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031005695
776 0 8 _iPrinted edition:
_z9783031028250
830 0 _aSynthesis Lectures on Computational Electromagnetics,
_x1932-1716
_985293
856 4 0 _uhttps://doi.org/10.1007/978-3-031-01697-4
912 _aZDB-2-SXSC
942 _cEBK
999 _c85790
_d85790