# Series or Physics?

A bar of length $$a$$ is at zero temperature. At $$t=0$$, the end $$x=a$$ is raised to a temperature $$u_0$$ and the end $$x=0$$ is insulated. If the temperature at any point $$x$$ of the bar at any time $$t>0$$, assuming that the surface of the bar is insulated, can be expressed as:

$\displaystyle u(x,t)=u_0+\frac{Au_0}{\pi^B}\sum_{n=1}^{\infty}\frac{(-1)^n}{(2n-1)}e^{-\frac{(2n-1)^C\pi^Dc^2t}{Fa^G}}\cos\left( \frac{(2n-1)\pi x^H}{Ia^J} \right)$

Evaluate $$A+B+C+D+F+G+H+I+J$$

Details and Assumptions:

Here, $$c$$ is arbitrary constant.

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