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I am going through the article at this link, where the author proves that $\pi$ is $\text{transcendental}$ over $\mathbb{Q}$. Although, I understand the proof, I have some doubts.

  • At page $6$, the author defines a new function $f(x)$ as $$f(x) = c^{s}x^{p-1} \frac{[\theta(x)]^{p}}{(p-1)!}$$ Can anyone tell me what is the motivation behind defining $f(x)$ in this manner.
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    [Crossposted to MO](http://mathoverflow.net/questions/78170/idea-behind-choosing-small-fx-as-csxp-1-frac-thetaxpp-1).2011-10-15

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