i need series representation for the equation of erfc(x) and maching with it in plot

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sura 2022-9-22

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https://ww2.mathworks.cn/matlabcentral/answers/1810435-i-need-series-representation-for-the-equation-of-erfc-x-and-maching-with-it-in-plot

评论： Torsten 2022-9-24

i need series representation for the equation of erfc(x) and maching with it in plot. there are series representation. taylor series is series expansion. in wolfram website (www.wolframalpha.com) you can write series erfc(x). you will find three or more series representation. i need one of these match with erfc(x) with function by k not x. like equation imges below (which one is good for matching plot figure )

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采纳的回答

Chunru 2022-9-23

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https://ww2.mathworks.cn/matlabcentral/answers/1810435-i-need-series-representation-for-the-equation-of-erfc-x-and-maching-with-it-in-plot#answer_1059080

在 MATLAB Online 中打开

x = 0.5; 
format long
erfc(x)
ans = 
   0.479500122186953
for n=1:20
    y(n) = erfc_by_series(x, n);
end
y'
ans = 20×1
   0.482826215081223
   0.479300030184050
   0.479509922142215
   0.479499719060915
   0.479500136459696
   0.479500121743713
   0.479500122199208
   0.479500122186648
   0.479500122186960
   0.479500122186953
function y= erfc_by_series(x, n)
   
    t = x;      % term inside sum for k=0
    s = t;
    for k=1:n
        t = -t*x.^2/k;
        s = s + t/(2*k+1);
    end
    y = 1 - 2/sqrt(pi)*s;
end