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Figure 3
(a) Error difference in evaluating h2(1)Y42 using (i) the standard product of the radial Hankel function h2(1) and spherical harmonic Y42 and (ii) the translational addition theorem (14)[link], (15)[link] at a distance [{\bf d}_{p} = (0,3,5)] (in normalized radii) from the origin with expansion order [\nu_{\max} = 10]. The circle represents spheres of radius 1. Colour axis in log scale. (b) Continuity error at the sphere boundaries [i.e. difference between the solution computed at the boundary using equations (4)[link] and (5)[link], integrated over the sphere boundary]. For this example, N = 4 and kamax = 4. The error reaches machine accuracy at expansion order [\nu_{\max} = 10].

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ISSN: 2053-2733
Volume 79| Part 2| March 2023| Pages 180-191
https://doi.org/10.1107/S2053273322011779
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