An extension of the Fock current distribution functions

Bowman, 1987 Franz, 1952, Theorie der Beugung am Zylinder unter Berucksichtigung der Kriechwelle, Ann Physik, 10, 361, 10.1002/andp.19524450606 King, 1959 Fock, 1946, The distribution of currents induced by a plane wave on the surface of a conductor, J Phys (USSR), 10, 130 Levy, 1959, Diffraction by a smooth object, Comm Pure Appl Math, 12, 159, 10.1002/cpa.3160120108 McNamara, 1990 Fock, 1965 Bouche, 1997 Molinet F, Andronov I, Bouche D. Asymptotic and hybrid methods in electromagnetics. London: IEE series EW 51; 2005. Melrose, 1985, Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle, Adv Math, 55, 242, 10.1016/0001-8708(85)90093-3 Atle, 2007, On surface radiation conditions for high-frequency wave scattering, J Comput Appl Math, 204, 306, 10.1016/j.cam.2006.02.045 Goriainov, 1958, An asymptotic solution of the problem of diffraction of a plane electromagnetic wave by a conducting cylinder, Radio Eng Electron (USSR), 3, 23 Logan NA. General research in diffraction theory. Technical Report vol. 1, LMSD-288087. Sunnyvale, CA: Lockheed Missiles and Space Division; 1959. Shore, 2001, Shadow boundary incremental length diffraction coefficients applied to scattering from 3-D bodies, IEEE AP, 49, 200, 10.1109/8.914277 Pearson, 1987, A scheme for automatic computation of Fock-type integrals, IEEE AP, 35, 1111, 10.1109/TAP.1987.1143985 Huybrechs, 2007, A sparse discretization for integral formulations of high frequency scattering problems, SIAM J Sci Comput, 29, 2305, 10.1137/060651525 Asheim, 2010, Local solutions to high-frequency 2D scattering problems, J Comput Phys, 229, 5357, 10.1016/j.jcp.2010.03.034 Friedlander, 1954, Diffraction of pulses by a circular cylinder, Comm Pure Appl Math, 7, 705, 10.1002/cpa.3160070407 Sandström, 2008, A remark on the computation of Fock functions for negative arguments, Int J Electron Commun (AEÜ), 62, 324, 10.1016/j.aeue.2007.08.001 Trefethen, 2008, Is Gauss quadrature better than Clenshaw-Curtis, SIAM Rev, 50, 67, 10.1137/060659831 Iserles, 2005, Efficient quadrature of highly oscillatory integrals using derivatives, Proc R Soc A, 461, 1383, 10.1098/rspa.2004.1401 Trefethen, 2006, Talbot quadratures and rational approximations, BIT Numer Math, 46, 653, 10.1007/s10543-006-0077-9 2009 Sandström, 2009, Computation of the Fock scattering functions Abramowitz, 1965 Olver, 1954, The asymptotic expansion of Bessel functions of large order, Philos Trans R Soc Lond A, 247, 328, 10.1098/rsta.1954.0021 Olver, 1997 Gil, 2007 Landau, 2000, Bessel functions: monotonicity and bounds, J Lond Math Soc, 61, 197, 10.1112/S0024610799008352 Fornberg, 1981, Numerical differentiation of analytic functions, ACM Trans Math Softw, 7, 512, 10.1145/355972.355979 Calio’, 1991, Numerical differentiation of analytic functions using quadratures on the semicircle, Comput Math Appl, 22, 99, 10.1016/0898-1221(91)90196-B Bornemann, 2011, Accuracy and stability of computing high-order derivatives of analytic functions by Cauchy integrals, Found Comput Math, 11, 1, 10.1007/s10208-010-9075-z Paris, 2004, On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals: II. Complex variable, J Comput Appl Math, 167, 321, 10.1016/j.cam.2003.10.021 Koutitas, 2006, A UTD solution for multiple rounded surfaces, IEEE AP, 54, 1277, 10.1109/TAP.2006.872675