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A joke in approximating numbers raised to irrational powers
Pade Approximations are cute
To get even closer to the actual result, I had to compute 8 terms for the series expansion, and no, it wasn’t by hand, as I’ve used WolframAlpha do it for me: The smart idea behind this technique is to distribute the control points of a polynomial between the denominator and the numerator of the rational function. \[f(x) \approx P_{[m,n]}(x)=\frac{a_0+a_1x+a_2x^2+\dots+a_mx^m}{1+b_1x+b_2x^2+\dots+b_nx^n}\] Compared to Taylor Series, Padé seem to handle exponential behaviors and discontinuities better, plus in a lot of cases it converges faster.
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