The most general solution for the equations of motion for Dirichlet is given by:

$$ X^{\mu}=a^{\mu}+\frac{1}{\pi}\left(b^{\mu}-a^{\mu}\right) \sigma+\sqrt{2 \alpha^{\prime}} \sum_{n \neq 0} \frac{\alpha_{n}^{\mu}}{n} e^{-i n \tau} \sin n \sigma $$

My question is: How do I get the $a^u_0$ mode from the boundary conditions?


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