This is the graph of the Bessel function of order 0, along with its asymptotic approximation for large x. You can see that the convergence is quite fast. The Bessel function is important in many problems in physics, from solutions of the Helmholtz equation in cylindrical coordinates (as in a vibrating drumhead) to many quantum mechanical systems.
In non-physics news, I saw The Dark Knight this weekend. Oh holy carp. Previously it was perfectly true to say that there were comic book movies which were legitimately good film - Spider Man 2, Sin City, a few others. There weren’t any that were actual Great Films, though. The Dark Knight rises to that level. I can’t speak highly enough of it. It makes the Batman Begins look like sunshine and bunnies.
2 responses so far ↓
1 Super Jesus // Jul 20, 2008 at 11:21 pm
I just got back from seeing it as well. I definitely need to make my kids watch it again when they’re 18 and will perhaps then understand how remarkable and appropriate this story was (especially given the current political climate). I need to see that again…soon.
2 Chuck // Jul 21, 2008 at 6:28 am
Problem with missing parentheses I think. Surely it should be cos(x - pi/4); the asymptotic value of J0 is 0, not pi/4.
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