Editor's Note:
Gergõ Nemes is a young Hungarian mathematician who is just starting in earnest his formal mathematical education. He has tried a functional transformation of the Stirling's asymptotic series going, without getting lost, through the messy chore of Faà di Bruno formula and came up with an interesting novel series. While Stirling's series is asymptotic (i.e., not convergent), the Nemes expansion might be actually convergent (at least for arguments greater than 1). Though this is not yet quite clear, I find very interesting the implication that a functional transformation might convert a nonconvergent asymptotic series into a convergent one.
I also like the 'closedform' formula in Section 5, which Gergõ just happened to notice and pick up while comparing his formula with that of Laplace. Considering its simplicity, it is amazingly accurate.
If you wish, download the Matlab program used to numerically test the various approximations and draw Figure 1.
