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4h
comment Don't understand about how to solve the first equation with Gauss Elimination
Alright, please pay attention to where you're posting the next time; saves you and I the bother.
4h
comment Don't understand about how to solve the first equation with Gauss Elimination
Didn't you notice where your other question was moved?
9h
revised Why is it that the Lambert W relation cannot be expressed in terms of elementary functions?
edited tags
14h
awarded  Yearling
1d
comment Chandrasekhar history
This should probably be asked in physics.SE or that new HSM.SE…
Jul
26
awarded  Good Answer
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
16
revised The ratio of jacobi theta functions
edited tags
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
revised Why is the Gamma function off by 1 from the factorial?
edited tags
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.)
Jul
15
comment Derivation of approximation of Error function
With respect to Winitzki: the reasoning is that you want to build a rational function (or any approximant, really) whose qualitative behavior at $0$ and $\infty$ is similar to $\mathrm{erf}(x)$; polynomials certainly cannot do that, since they cannot exhibit asymptotes as in this case.
Jul
15
comment Derivation of approximation of Error function
Ah, that parameter I am not too sure of; Cecil Hastings was (in)famous for coming up with clever approximations that seemed to have just come from thin air.
Jul
15
comment Conditions on Matrix invertibility
I was nudging you to search for them yourself, as I have now given you the words you should be looking for.
Jul
15
comment Derivation of approximation of Error function
Let's call the polynomial in your expression $p(t)$; you can rearrange your formula to obtain $\exp(x^2)\mathrm{erfc}(x)\approx p(t)$. Replace the $x$ on the left with an expression in terms of $t$. That is the function which you will be approximating as a series in Chebyshev polynomials. You might want to look up the literature on this, including "economization" of series.
Jul
15
comment Derivation of approximation of Error function
That was one of his papers; there was another one that specially dealt with $\mathrm{erf}$.
Jul
15
comment Conditions on Matrix invertibility
There are methods for updating the QR decomposition and singular value decomposition when a new column or row is added to the original matrix; you might want to look them up.