Would someone help me understand the way the solution obtained in this question: Heat Equation Mixed Boundaries Case: Fourier Coefficients
I did not understand why in the final solution, he took $b_m$ and not $b_{2m-1}$. I am confused not just because of the rank of the coefficients, this is because according to this rank $$b_m= \frac{1}{L} \int_{0}^{2L} f(x) sin\Big(\frac{m \pi x}{2L}\Big)$$ or $$b_{2m-1}= \frac{1}{L} \int_{0}^{2L} f(x) \sin\Big(\frac{(2m-1) \pi x}{2L}\Big)$$
Sorry if I appear much confused, but I really want to understand it. Thanks in adavnce.