I'm interested in inverting a power series: Suppose through solving a DE for the function y(x), I ended up with a power series in y:
Now, we know
I'm just learning I can invert that series to obtain:
But each derivative in y is related to each derivative in x by the recursive formula:
and therefore if I know what each is, I can recursively calculate the coefficients
Here's the first few:
You guys think it's possible to figure out a non-recursive formula for ?
I can begin to see a trend for :