Uniform Stationary Phase MethodInstitution of Electrical Engineers, 1994 - 233 pages This monograph expounds an original asymptotic stationary phase method for the evaluation of integrals of rapidly oscillating functions, which should be beneficial in wave radiation, propagation and diffraction research. It is self-contained, with theory, formulae and tabulated co-efficients. |
Table des matières
Asymptotic contribution of critical point in onedimensional | 7 |
Two critical points merging in a onedimensional integral | 30 |
24 | 49 |
Droits d'auteur | |
6 autres sections non affichées
Expressions et termes fréquents
Airy function analytical function angle aperture asymptotic eqn asymptotic expansion asymptotic of eqn asymptotic of I(2 asymptotic series bounded in magnitude branch point C₁ caustic co-ordinates coefficients complex conjugate condition Consider contribution corner point critical points cutting function diffraction dx dy edge wave edge-wave equation evaluate exp ix² expressed in terms Ff(x field U(M Fresnel integral function f(x geometrical optics Helmholtz equation incident wave integral I(2 integral sine integration contour integration domain boundary interval Kirchhoff approximation leading term light-shadow boundary nonexponential factor nonuniform asymptotic observation point obtains parabolic cylinder functions phase function phase-function stationary point Piercey integral pole primary field prove eqn reflected field refracted region supp second derivative sin² special functions stationary phase method stationary point summand tends to zero theorem transient zones U₁ uniform asymptotic variable change vicinity wedge x=xo αξ