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Benedict Irwin edited Explicit Derivative.tex
over 9 years ago
Commit id: 92eb8704676a4ec935eca9aa529590effdaa2410
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On another note, it was seen that $q=\pi a^2/2$ and then with increasing $a$ the approximation improves. (However the power will increase drastically, and therefore require some computation. Therefore, in the limit $a \to \infty$ we can to some extent guess that \begin{equation}
\frac{(1-\frac{x^2}{a^2})^{\pi a^2/2}(a^6-x^6)}{(a^6+x^6)} \lim_{a \to \infty}\frac{(1-\frac{x^2}{a^2})^{\pi a^2/2}(a^6-x^6)}{(a^6+x^6)}= e^{-\pi x^2/2}
\end{equation}