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Let $$ Q = \begin{bmatrix} Q_0 & Q_1 & Q_2 & \cdots\\ Q_{-1} & Q_{0} & Q_1 & \cdots\\ Q_{-2} & Q_{-1} & Q_0 & \cdots\\ \vdots & \vdots & \vdots & \ddots ...

In order to solve a boundary problem for a conducting hemisphere, the following matrix equation arises (derived from the boundary condition on the curved part of the surface) where we must solve for ...