I created a method for both approximating a function and extending a it's domain from a Natural to a Real Domain. Does this have a name already or any interesting application? Basically. Add polynomial of degree 0, 1, 2, 3, etc. Making at the same time the approximation function equal to f(0), f(1), f(2), f(3), etc. The approximation of function f is: App. of f http://latex.codecogs.com/examples/a0d1659d13fd1904ffe767edc6cab6e4.gif [Broken] n is level of the approximation, the bigger the n the bigger the approximation and the more the polynomia. http://latex.codecogs.com/examples/10d3e8addce0f1cea366f3eafcae03df.gif [Broken]=f(n)-App. of f at n of level (n-1) http://latex.codecogs.com/examples/00d8763b00aac3dd87168ec5039ec758.gif [Broken] http://latex.codecogs.com/examples/92cf5169e1dbb1a99d49de59187bc652.gif [Broken] etc. The idea is actually very simple! Just add a constant and then a line and then a parabola, etc to make it similar to the function. Also can anyone find a simpler way to find the coefficients. E? Maybe for f(x)=x! ?