MHB Solve for A_n: Fourier Coefficient $$u_y(x,\pi) = 0$$

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The equation presented is \(u_y(x,\pi) = \frac{x}{\pi} + \sum_{n = 1}^{\infty}nB_n\sin xn\cosh\pi n = 0\). The user seeks to solve for \(A_n\), but a clarification indicates that \(B_n\) is the correct term, as there is no \(A_n\) in the equation. The focus of the discussion is on understanding the Fourier coefficients and their relation to the given equation. The conversation highlights the importance of correctly identifying terms in mathematical expressions. Accurate identification of variables is crucial for solving such equations effectively.
Dustinsfl
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$$
u_y(x,\pi) = \frac{x}{\pi} + \sum_{n = 1}^{\infty}nB_n\sin xn\cosh\pi n = 0.
$$
How can I solve for $A_n$ here?
 
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dwsmith said:
$$
u_y(x,\pi) = \frac{x}{\pi} + \sum_{n = 1}^{\infty}nB_n\sin xn\cosh\pi n = 0.
$$
How can I solve for $A_n$ here?

Hi dwsmith, :)

You you mean \(B_n\) ? There is no \(A_n\) in the equation.

Kind Regards,
Sudharaka.
 
We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.

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