Benedict Irwin edited section_Another_Result_begin_equation__.tex  almost 8 years ago

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\section{Another Result}  \begin{equation}  \lim_{N\to\infty}\left(\sum_{k=1}^N x^{x^{p_k}}\right)-N=\sum_{q=2}^\infty \left(\sum_{p|q} \frac{\log(x)^{q/p}}{\left(\frac{q}{p}\right)!}\right)x^q \frac{\log(x)^{q/p}}{\left(\frac{q}{p}\right)!}\right)x^q\\  \lim_{N\to\infty}\left(\sum_{k=1}^N x^{x^{p_k}}\right)-N= \sum_{p\in\mathbb{P}} \sum_{q=1}^\infty \frac{\log(x)^qx^{qp}}{q!}  \end{equation}  where $p$ is a prime, and $p_k$ is the $k^{th}$ prime.