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Jun 19, 2018 at 10:15 comment added Gro-Tsen @RomainGicquaud The thing about numerical integration is that (A) the wave fronts $t\pm\theta=2k\pi$ seem just as problematic in this approach, and (B) this seems more suited to producing values of various $(\theta,t)$ as opposed to fixed $\theta$ and many $t$'s. (Of course, it is possible that there is no good answer to my question.) But I certainly agree that summing the (divergent!) series is not a good approach; it is how I computed the approximate graph, however.
Jun 19, 2018 at 10:08 comment added Romain Gicquaud 0 down vote I do not know the answer but trying to sum the formula you have is a bad idea. You should instead write the wave equation in polar coordinates and try to integrate this equation.
Jun 19, 2018 at 9:42 history edited Gro-Tsen CC BY-SA 4.0
add an approximate graph for a quarter-turn angle
Jun 18, 2018 at 22:53 history asked Gro-Tsen CC BY-SA 4.0