Question: Starting with the series solution (2.71) for the two-dimensional potential problem with the potential specified on the surface of a cylinder of radius b, evaluate

Starting with the series solution (2.71) for the two-dimensional potential problem with the potential specified on the surface of a cylinder of radius b, evaluate the coefficients formally, substitute them into the series, and sum it to obtain the potential inside the cylinder in the form of Poisson's integral:

b? – p² b? + p? — 2bp cos(ф' - ф) dф' Ф(ь, ф') Ф(р, ф) 2т

What modification is necessary if the potential is desired in the region of space bounded by the cylinder and infinity?

b? p b? + p? 2bp cos(' - ) d' (, ') (, ) 2

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