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Chapter 12: Q 7-5P (page 562)
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Expand the following functions in Legendre series.
Substitute the Pl(x), you found in Problems 4.3 or 5.3into equation (10.6)to find Plm(x) then let x=cosθ to evaluate:
P11(cosθ)
To study the approximations in the table, a computer plots on the same axes the given function together with its small approximation and its asymptotic approximation. Use an interval large enough to show the asymptotic approximation agrees with the function for large . If the small approximation is not clear, plot it alone with the function over a small interval .
Verify that the differential equation in Problemis not Fuchsian. Solve it by separation of variables to find the obvious solutionconst. and a second solution in the form of an integral. Show that the second solution is not expandable in a Frobenius series.
Show that
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