Mellin-transform method for integral evaluation

Mellin-transform method for integral evaluation

by Fikioris, George J.

Type Book
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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…

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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.

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Edition Statements

  • Publication Date:©2007.
  • Edition:1st ed

Publication Statements

  • Publisher(s):Morgan & Claypool Publishers
  • Place of Publication:San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA)
  • Language:eng
  • Publication Date:©2007.

Notes

A printed version of a work that appears in the 'Synthesis digital library of engineering and computer science'.

Title from PDF title page (viewed October 19, 2008).

The Physical Object

  • Description:1 online resource (78 pages)

Edition Identifiers

Table of 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 -- …

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Subjects

Antennas (Electronics) -- Mathematical … Antennes (Électronique) -- Modèles math… Mellin transform Transformation de Mellin

Writers

Fikioris, George J.

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