How to code Taylor's series approximation of Error function? Is following code right? Please help

z=0:4; ert=zeros(1,length(z)); sm=zeros(1,length(z)); sm=0; for k=1:length(z) for n=0:500 sm=sm+((-1)^n*z(k)^(2*n+1))/(gamma(n-1)*(2*n+1)); end ert(k)=(2/sqrt(pi))*sm; end

Answer 1

[Torsten]

Although the coding is not optimal, it looks ok.

Why don't you just compare "ert(k)" and erf(z(k)) to get an answer to your question ?

Best wishes

Torsten.

[Priya Khot]

if true
  % code
end
In the above code, I've compared answers with inbuilt 'erf' MATLAB command answers. I'm getting correct answers only for 0 to 3 after that m getting NaN.

Answer 2

[Torsten]

You must avoid to explictly calculate z^(2*n+1)/n!.

For large n and |z|>1, you'll get an infinity/infinity problem.

Use that

[(z^2)^n/n!] = [(z^2)^(n-1)/(n-1)!] * (z^2/n).

Thus, you can calculate summand (n) of the series from summand (n-1) instead of recalculating every summand anew.

Best wishes

Torsten.