How can I write the taylor series expansion for the function (1+x^2)^(-1/2) in code

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JoshT_student 2018-7-5

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评论： Torsten 2018-7-6

20180705_092556.jpg

Hello. I am trying to get this taylor series expansion in code but I am having a hard time. I attached a picture of the function and its taylor series expansion. I thought of using the factorial function but I don't think that will work here. Thank you for the help.

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Geoff Hayes 2018-7-5

Joshua - no, you probably don't need to use the factorial function here. But from what you have shown, what is the pattern? Once you figure that out then the expansion should be easy.

JoshT_student 2018-7-5

Thank you Geoff.

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Torsten 2018-7-5

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编辑：Torsten 2018-7-5

在 MATLAB Online 中打开

    a0 = 1
    an = -a(n-1) * (2*n-1)/(2*n)

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JoshT_student 2018-7-5

Thank you Torsten, now to get 50 terms of it, I just need to put it in a for loop?

Torsten 2018-7-6

在 MATLAB Online 中打开

x=0.5;
f=1.0;
a=1.0;
xn=1.0;
n=25;
for i=1:n
  a=-a*(2*i-1)/(2*i);
  xn=xn*x^2;
  f=f+xn*a;
end

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