Find a formula for the temperature u(x,t) in the form of a series with general formula for the coefficients of the series.

\alpha^2 \frac{ \partial^2 u}{ \partial x^2} = \frac{\partial u}{\partial t} and 0<x<L ; t>0

u(0,t) = 0 and \frac{\partial u}{\partial x}(L,t) = 0 and t>0

u(x,0) = f(x)


f(x) is assumed to be piecewise continuous and periodic of period 2L