Continuous function?

1. Mar 25, 2009

thegaussian

Hi. I'm looking to at how expectation values of periodic functions evolve in time, and i need to prove that <Exp[i$$\theta$$]> is continuous in time (this is the expectation of the exponential of the angle).
My formula is:

<Exp[i$$\theta$$]> = Exp[it$$/$$2]$$\sum$$ana*n-1Exp[-int]

where an 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!