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Chapter 12: Q8-2P (page 562)
Find the norm of each of the following functions on the given interval and state the normalized function
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To study the approximations in the table, a computer plot on the same axes the given function together with its small x approximation and its asymptotic approximation. Use an interval large enough to show the asymptotic approximation agreeing with the function for large x. If the small x approximation is not clear, plot it alone with the function over a small interval
Solve to get . If needed, see Chapter , Section 2. The given equation
Verify equation (18.3) i.e.
Expand the following functions in the Legendre series.
Show that dl-m/dxl-m (x2-1)l=(l-m)!/(l+m)! (x2-1)m dl+m/dxl+m (x2-1)l.
Hint: Write(x2-1)l=(x-1)l(x+1)land find the derivatives by Leibniz' rule.
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