Implementing Fisher Scoring Recursively

Hi, and welcome!

Please see the FAQ: What's a reproducible example (`reprex`) and how do I create one? Using a reprex, complete with representative data will attract quicker and more answers.

Your question doesn't really need one (and due to the error, couldn't be produced, anyway) since there are no libraries to be loaded and no data. Still, it helps to enclose in triple backticks to make it easier to cut and past

fs_pois <- function(data, true, guess) {
if (abs(guess-true) < 0.01) return(guess)
else return(fs_pois(data, true, guess + (mean(data)*exp(-guess))-1))

data <- rpois(100,lambda=0.34)
fs_pois(data, 0.34, 0.36)

The code produces

Error: C stack usage 7969568 is too close to the limit

This is an operating system constraint that this S/O post addresses for the *nices. Don't think I can help you on windows.