Investigate the formulas involving `alpha`

[stla]

See here and here.

I don't remember why I use these transformation formulas. And I'm wondering whether they should be swapped (following an observation during the development of my Haskell package; I fixed a failure by swapping these two lines).

@simonp0420 Do you remember why I use these formulas? Why not using the "direct" formulas, without these transformations involving the alpha function?

[simonp0420]

I think this was added when you were reviewing my original PR. See this comment.

[stla]

Thanks. I didn't read yet. I've just tried to replace these formulas in my R package with the "direct" formulas and some unit tests have failed, those related to some Weierstrass functions. So it looks like these formulas have an advantage. Need to investigate more.