I am going through the article at this [link][1], 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. 






  [1]: http://sixthform.info/maths/files/pitrans.pdf