I have a problem. My company has given he an awfully boring task. We have two databases of dialog boxes. One of these databases contains images of horrific quality, the other very high quality.
Unfortunately, the dialogs of horrific quality contain important mappings to other info.
So I have be...
On a more serious note, anyone here familiar with elliptic integrals? I have an integral where mma pops out an EllipticK as the result, but I'm trying to figure out where to start so that I can get to it with pencil and paper (the answer almost always involves Abramovitz and Stegun)
@acl I know the final answer. I need to work out the intermediate steps so that I can "derive" it in an appendix. So I need to know a reasonable starting point
@R.M in seriousness, I'd say that A&S is really not a book to look up integrals. it's for properties of functions. G&S is explicitly a catalog of integrals, arranged so that you can look things up
but in your case, you basically know you need to bring your integral into the form that is the definition of K, so you just have to manipulate it until you get that
or, from this form, you can write $I_n=\int dx \exp(-2x)J_n(x)^2$ and obtain a recurrence relation between the $I_n$ (by integrating by parts) and try to look up the solution to that
or other things. there's an infinite number of ways to waste time with these things
@R.M I see. Since asymptotically $J_0(x)$ decays like $1/\sqrt{x}$ and it is everywhere bounded on the real line it seems obvious, but I guess standards of rigour differ in different areas!
Yes, the obvious argument why I've been ignoring it until now when I'm writing it down, but since it isn't obvious to the audience I'm writing to, I'll have to expand on it a little.
For Example
s = Table[k[j] -> Interpolation[Table[{i, Sin[i j]}, {i, 6}]], {j, 1, 6}];
Manipulate[
ParametricPlot3D[{{k[4][t], k[5][t], k[6][t]}, {k[1][t], k[2][t], k[3][t]}} /. s, {t, 1, a},
PlotStyle -> {Red, Green},
Evaluated -> True,
PlotRange -> {{-1.5, 1.5}, {-1.5, 1...
