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Benedict Irwin edited section_Closed_Forms_from_Mathematica__.tex
over 8 years ago
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\section{Closed Forms from Mathematica}
Mathematica seems to offer closed forms for some of the expressions above. For example
\begin{equation}
\frac{\left[\underset{k=1}{\overset{\infty}{\large \left[\underset{k=1}{\overset{\infty}{\large K
\normalsize}} \normalsize} \frac{1}{x} = \frac{2}{x+\sqrt{4+x^2}}\\
\frac{\left[\underset{k=1}{\overset{\infty}{\large \left[\underset{k=1}{\overset{\infty}{\large K
\normalsize}} \normalsize} \frac{n}{x} = \frac{2n}{x+\sqrt{4n+x^2}}
\end{equation}
where we then see that the Laurent expansion does indeed follow the form \begin{equation}
\lim_{x\to\infty}\frac{2}{x+\sqrt{4+x^2}}=\sum_{k=1}^\infty \frac{C(k)}{x^{2k+1}}