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Novel exact and asymptotic series with error functions, for a function involved in diffraction theory: the incomplete Bessel function

Presented by: 
J.M.L. Bernard ENS de Cachan
Date: 
Monday 12th August 2019 - 14:00 to 14:30
Venue: 
INI Seminar Room 1
Abstract: 
The incomplete Bessel function, closely related to incomplete Lipschitz-Hankel integrals, is a well known known special function commonly encountered in many problems of physics, in particular in wave propagation and diffraction [1]-[5]. We present here novel exact and asymptotic series with error functions, for arbitrary complex arguments and integer order, derived from our recent publication [5].  

[1] Shimoda M, Iwaki R, Miyoshi M, Tretyakov OA, 'Wiener-hopf analysis of transient phenomenon caused by time-varying resistive screen in waveguide', IEICE transactions on electronics, vol. E85C, 10, pp.1800-1807, 2002
[2] DS Jones, 'Incomplete Bessel functions. I', proceedings of the Edinburgh Mathematical Society, 50, pp 173-183, 2007
[3] MM Agrest, MM Rikenglaz, 'Incomplete Lipshitz-Hankel integrals', USSR Comp. Math. and Math Phys., vol 7, 6, pp.206-211, 1967
[4] MM Agrest amd MS Maksimov, 'Theory of incomplete cylinder functions and their applications', Springer, 1971.
[5] JML Bernard, 'Propagation over a constant impedance plane: arbitrary primary sources and impedance, analysis of cut in active case, exact series, and complete asymptotics', IEEE TAP, vol. 66, 12, 2018
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons