Hi. I'm looking to at how expectation values of periodic functions evolve in time, and i need to prove that <Exp[i[tex]\theta[/tex]]> is continuous in time (this is the expectation of the exponential of the angle).(adsbygoogle = window.adsbygoogle || []).push({});

My formula is:

<Exp[i[tex]\theta[/tex]]> = Exp[it[tex]/[/tex]2][tex]\sum[/tex]a_{n}a*_{n-1}Exp[-int]

where a_{n}are the fourier coefficients of the initial function, * represents the complex conjugate and the sum is over n from -infinity to infinity. Now how do I go about proving it's continuous? We have basically a complex exponential factor (that's obviously continuous) multiplied by a fourier series, but I just have no idea really where to go from there.

Any help would be much appreciated.

Thanks!

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# Continuous function?

Can you offer guidance or do you also need help?

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