Book ChapterDOI
Fourier and laplace transforms
I.S. Gradshteyn,I.M. Ryzhik +1 more
- pp 1142-1153
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In this paper, the Fourier and Laplace transform integrals are discussed and the inversion integral is used for analytic functions of order O(p -k ) with k > 1.Abstract:
This chapter discusses Fourier and Laplace transforms. The inversion of the Laplace transform is accomplished for analytic functions f (p) of order O (p -k ) with k > 1 by means of the inversion integral. The inversion of the Fourier transform is accomplished by means of the inversion integral. The Fourier sine and cosine transforms of the function f(x), denoted by F s (ξ) and F c (ξ), respectively, are defined by the integrals. The functions f(x) and F s ( ξ ) are called a Fourier sine transform pair, and the functions f(x) and F c ( ξ ) a Fourier cosine transform pair, and knowledge of either F s ( ξ ) or F c ( ξ ) enables f(x) to be recovered. The inversions of the Fourier sine and Fourier cosine transform are accomplished by means of the inversion integral.read more
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de Haas–van Alphen effect in two- and quasi-two-dimensional metals and superconductors
TL;DR: In this article, an analytical form of the quantum magnetization oscillations (de Haas van Alphen effect) is derived for two-and quasi-two-dimensional metals in normal and superconducting mixed states.
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Generalisations of the Laplace-Runge-Lenz vector
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Generalisations of the LaplaceRungeLenz Vector
P. G. L. Leach,G. P. Flessas +1 more
TL;DR: The characteristic feature of the Kepler Problem is the existence of the so-called Laplace-Runge-Lenz vector which enables a very simple discussion of the properties of the orbit for the problem as discussed by the authors.
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Electrostatic Image Theory for the Dielectric Prolate Spheroid
Ismo V. Lindell,Keijo Nikoskinen +1 more
TL;DR: In this paper, a point charge at the axis of revolution of a dielectric prolate spheroid is represented as a line charge between the two focal points of the sphroid in terms of the Legendre series.
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Mixed-potential Green's functions for sheet electric current over metal-dielectric cylindrical structure
TL;DR: In this paper, an efficient numerical-analytical approach is developed to calculate spatial mixedpotential Green's functions for sheet currents placed over a cylindrical circular metal rod with a dielectric substrate.