I was wondering how this publication gets the following answer for this derivation?
Equation being solved:
$$C_o-C_m(x,t)=\frac{2I_ot^{1/2}}{FAD^{1/2}}\sum^\infty_{n=0}$$ $$\left[\text{ierfc}\frac{2(n+1)L-x}{2(Dt)^{1/2}}+\text{ierfc}\frac{2nL+x}{2(Dt)^{1/2}}\right]$$
Boundary Conditions and Assumptions:
.
I thought the function in the summation was the inverse complementary error function ierfc, but I can't seem to get the $\frac{1}{\sqrt{\pi}}$ term from its Integral. If I have two ierfc terms, don't I add the infinite summations of both, giving me $\frac{2}{\sqrt{\pi}}$?
How does the solution change if instead of my original boundary condition $C_m(0,t_0) = 0, x = 0, t = t_0$ it changes to: $C_m(L,t_0) = 0, x = L, t = t_0$?