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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.)