math whizzes: where do the magic numbers in the horner's method solution for an error function come from?https://github.com/simple-statistics/simple-statistics/issues/355 …
Here's a screenshot from a newer edition of NR which is a little more explicit than "inspired guess". The important part is that for all positive z, t is between 0 and 1. This makes the function P(t) suitable for approximation by Chebyshev polynomials https://en.wikipedia.org/wiki/Chebyshev_polynomials …pic.twitter.com/6UPkIHfe3l
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A long and boring computation that I am not up for ought to confirm that the magic numbers arise from doing a 9th order (the final polynomial is degree 9) Chebyshev approximation to the function P(t) there.
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