COS(2pix)

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

Answer 1

[Walter Roberson]

    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?

Answer 2

[Fawaz Hjouj]

Isnt this series convergent?

[Walter Roberson]

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]

Who is "Wally"?

[Steven Lord]

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 :)

Answer 3

[Fawaz Hjouj]

Sorry wrong person