For an alternative approach, if you treat this function as a time series where x is time, you can get a reasonably good approximation by performing SVD of the t

For an alternative approach, if you treat this function as a time series where x is time, you can get a reasonably good approximation by performing SVD of the trajectory matrix and building the forecast from the principal components (eigen vectors) using a recurrent formula. Here's an example: https://apps.axibase.com/chartlab/9922f98f https://apps.axibase.com/chartlab/9922f98f * Chart 1. Function value for x in [0, 1). * Chart 2. Function value for x in [0, 2). * Chart 3. Function value for x in [0, 1) and extrapolated values for x in [1, 2).