e^x = sum_n x^n/n! = 1 + x + (x^2)/2 + (x/3)/6... = 1 + x(1 + (x/2)(1 + (x/3)(1 +... exp(x,n) = 1 + (x/n)*exp(x,n+1) this gives you the exponential function

e^x = sum_n x^n/n! = 1 + x + (x^2)/2 + (x/3)/6... = 1 + x(1 + (x/2)(1 + (x/3)(1 +... exp(x,n) = 1 + (x/n)*exp(x,n+1) this gives you the exponential function as a recursion formula. Just set some condition for when to truncate. From there, a recursive function that does the exact opposite is easy enough. I'm sure there are optimizations you can do on top in the case that you don't get convergence within the first few terms.