Mellin-transform method for integral evaluation
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…
Read More ↓Title Statements
- Full title :Mellin-transform method for integral evaluation / George Fikioris.
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.
Read More ↓Edition Statements
- Publication Date:©2007.
- Edition:1st ed
Publication Statements
- Publisher(s):Springer
- Place of Publication:Cham, Switzerland
- Language:eng
- Publication Date:©2007.
Notes
Title from PDF title page (viewed March 7, 2007).
The Physical Object
- Description:1 online resource (ix, 67 pages)
Edition Identifiers
- ISBN:1598291858, 9781598291858, 9781598294439, 1598294431, 9783031016974, 3031016971
- DOI:10.1007/978-3-031-01697-4
- oclc:ocm85785265
- LC Classification:TK7871.6
- Dewey Decimal:621.381/331
Table of Contents
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…
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