Re: Taylor expansion using the fft

[Fernando]

Forgot to mention you can do numerical differentiation also using the same
code as above by adding:

deriv =coeff.*factorial(n));

which gives you up to the (N-1)th derivative evaluated at x=0.

Example:
taylor(16,0.5,@(x) exp(4*x))
deriv =coeff.*factorial(n))

ans =

 Columns 1 through 6:

   1.0000e+00   4.0000e+00   1.6000e+01   6.4000e+01   2.5600e+02  
1.0240e+03

 Columns 7 through 12:

   4.0960e+03   1.6384e+04   6.5536e+04   2.6214e+05   1.0486e+06  
4.1943e+06

 Columns 13 through 16:

   1.6777e+07   6.7109e+07   2.6844e+08   1.0737e+09

The first value in the outcome gives you the value of function at zero, and
then the first deriv, 2nd etc...

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