How would a mere mortal could possibly divine equations like this?
There is a method behind it. The formulas are derived from the study of relatively simple ODEs, in this example f'(x) = x.f(x) + 1 and g'(x) = x.g(x) − 1. The latter was solved 100 years prior by Jacobi. While the solutions are non-trivial, they are fairly compact, accessible to a high schooler. The presentation linked from the blog is pretty good at unveiling the magic.
This is to say that, with proper guidance, the kid down the street can too become as cool as Ramanujan.
There is a method behind it. The formulas are derived from the study of relatively simple ODEs, in this example f'(x) = x.f(x) + 1 and g'(x) = x.g(x) − 1. The latter was solved 100 years prior by Jacobi. While the solutions are non-trivial, they are fairly compact, accessible to a high schooler. The presentation linked from the blog is pretty good at unveiling the magic.
This is to say that, with proper guidance, the kid down the street can too become as cool as Ramanujan.
https://math.ucr.edu/home/baez/ramanujan/ramanujan_whittier_...