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The first two equations in the sequence, obtained by using (4.91) in (4.90), are

and (4.92a) has the general solution

with

Equation (4.92b) can then be written

which has the general solution

A solution that is uniformly valid as requires

and so, incorporating the boundary conditions, (4.94), we readily obtain

Combining this with (4.93), we have the first term of a uniformly valid representation
of the solution:

which should be compared with the solution obtained in Q2.17(a).