0 个投票

Hi ALL,
I needed the Taylor series ( about x=0) of cos[2*pi*x] for some application.
I wrote this little simple code:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Xvalue= -10:.01:10;
Yvalue =zeros(1, length(Xvalue));
for w =1: length(Xvalue)
x0=Xvalue(w);
ss=0;
for mm = 0:100
ss=ss+ (-1)^(mm ) * ((2*pi*x0)^(2*mm)) / factorial(2*mm) ;
end
Yvalue(w)=ss;
end
figure(1)
plot(Xvalue, Yvalue)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
I got the below figure, where after x is about =6, the y values started to be NAN.
comments please

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Walter Roberson
Walter Roberson 2019-8-28

0 个投票

for mm = 0:100
ss=ss+ (-1)^(mm ) * ((2*pi*x0)^(2*mm)) / factorial(2*mm) ;
What is (2*pi*6)^(2*100) ?
What is factorial(2*100) ?
What is the ratio of those two?

更多回答（2 个）

Fawaz Hjouj
Fawaz Hjouj 2019-8-28
编辑：Fawaz Hjouj 2019-8-31

0 个投票

Isnt this series convergent?

3 个评论
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Walter Roberson
Walter Roberson 2019-8-28
The value might be 0 in the limit, but you are not working in the limit, you are working with floating point numbers with finite precision and you are overflowing that finite precision.
Note the calculating the product of (2*pi*x0)^2 / (2*M) over M=0:100 would not suffer from the same overflow .
Walter Roberson
Walter Roberson 2019-8-29
Who is "Wally"?
Steven Lord
Steven Lord 2019-8-29
According to Wikipedia "Wally or Wallie is a given name, and a nickname for Wallace which ultimately means 'Wales' and Walter."
I don't recognize many of the real people listed on that Wikipedia page; I recognized many more from the Fictional characters section :)

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