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How to find a fourier series of a sawtooth function?

Alan Smith
Posted 9 years ago

I want to check my solution to this, the problem is

f(x) =\left{ -\frac{1}{2} (\pi+x), -\pi \le x < 0 , and \frac{1}{2} (\pi-x),0 < x \le \pi \right}

I have no idea how to write this so I can solve it in Mathematica?

I can't even write it here - it always looks OK in preview, but looses part of the eqtn when posted, which is why I took the $'s out

Thanks
POSTED BY: Alan Smith
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Alan Smith
Alan Smith
Posted 9 years ago

Thanks SM, that's much closer. Should I conclude that there is nothing in Wolfram that would return a simplified/rationalised solution? In this case I was checking a result that I knew was at least close, but - for example - if I wanted a simple function out of a Fourier expansion rather than doing it analytically, I probably wouldn't know anything about it's likely form ....
POSTED BY: Alan Smith

You could try

In[7]:= FourierSinSeries[f[x], x, 5]

Out[7]= Sin[x] + 1/2 Sin[2 x] + 1/3 Sin[3 x] + 1/4 Sin[4 x] + 
 1/5 Sin[5 x]

This implies that f(x)=Sum(n=1 to infinity) sin(nx)/n
POSTED BY: S M Blinder

Thanks, that specifies the function, but I want the output in the form: Sum (n=0 t inf) (sin x)/n ?
POSTED BY: S M Blinder
Alan Smith
Alan Smith
Posted 9 years ago

Thanks, that specifies the function, but I want the output in the form: Sum (n=0 t inf) (sin x)/n ?
POSTED BY: Alan Smith
POSTED BY: S M Blinder
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