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15h
comment Overlapping Polynomials
Consider what happens if you subtract the two "overlapping" polynomials. Unless the result is the zero polynomial, this violates the fundamental theorem of algebra.
2d
comment Common Math Mistakes Made by Scientists
+1; Kahan has talked about how a number of classical formulae perform very poorly when implemented numerically; his website has a number of examples.
2d
comment Can Eisenstein Series output complex numbers?
I see; I had used the formula relating $E_2$ and the complete elliptic integral of the second kind (from Abramowitz and Stegun), but wound up with a function that inherited the branch cuts of $E(m)$; I'll test your route the next time I have a computer…
Aug
26
comment Can Eisenstein Series output complex numbers?
Hi, may I ask what you used for making these plots? They look lovely.
Aug
20
comment How to convert a decimal to a fraction easily?
"and reduce" - would you be able to do the Euclidean algorithm quickly in a pinch?
Aug
20
comment How do 3 points define a plane?
...three noncollinear points, yes. In proper Euclidean geometry, this is actually a postulate.
Aug
17
comment Is there an equation to describe regular polygons?
You're basically using $\arctan \cot x$ here as your sawtooth… :)
Aug
17
comment Is there an equation to describe regular polygons?
What is the difference between this and Raskolnikov's answer?
Aug
17
comment Derivation of approximation of Error function
Antoine, I will need to review this again, which will take some time. It has admittedly been a while since I've ever had to manipulate Chebyshev series for approximation purposes…
Aug
16
comment Why does L'Hôpital's rule work for sequences?
possible duplicate of Is there a discrete version of de l'Hôpital's rule?
Aug
11
comment Problem with Integration using substitution
If you differentiate both of your results, do you get the original function?
Jul
31
comment Analytical approximation of integral of Bessel function
@Raymond, I pop up every so often here, yes, but sadly not as much as before. Yes, that was the answer I had in mind. :)
Jul
31
comment Analytical approximation of integral of Bessel function
For numerics, you can use a particular integral representation of the Bessel function that can be efficiently evaluated with the trapezoidal rule. I've posted this on this site some time in the past; search around.
Jul
28
comment Chandrasekhar history
This should probably be asked in physics.SE or that new HSM.SE…
Jul
19
comment Derivation of approximation of Error function
I might come back to it later. For now: why are you using the asymptotic series and not the Maclaurin series? That's not what I told you to do.
Jul
17
comment Rolling parabola & catenary
possible duplicate of Why does the focus of a rolling parabola trace a catenary?
Jul
15
comment Second derivative numerical estimate - stability and approach
…nice only if the underlying function is smooth. If OP's discrete samples have some error in them, Richardson does no good.
Jul
15
comment Derivation of approximation of Error function
I'm now telling you to try the economization procedure. Again: Maclaurin, convert to Chebyshev, truncate, and go back to the monomials. You should then see something like what Mr. Hastings had, or better. Abramowitz and Stegun should have the table for converting monomials to Chebyshev.
Jul
15
comment Derivation of approximation of Error function
Well, binomial won't get you anywhere near Mr. Hastings. If you'd tried looking up the things I told you to look up, you'd have already read about the "equi-ripple" and "minimax" properties of a Chebyshev approximation…
Jul
15
comment Derivation of approximation of Error function
Well, have you tried expanding the transformed function as a Maclaurin series, and re-expressing the monomials in Chebyshev terms? (As I said earlier, look up Chebyshev economization.)