Exercise 19.  Use the ML inequality to show that  ,  where    is the    Legendre polynomial defined on    by  

                      

Solution 19.

See text and/or instructor's solution manual.

Solution.  The absolute value of the integrand is  

                      
The maximum of this expression occurs when  .  

Now simplify    and apply the ML inequality.  

                      

Explore Solution 19.

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(c) 2008 John H. Mathews, Russell W. Howell