186 PROFESSOR A. E. H. LOVE ON THE 



* 



By these equations p is left arbitrary, and p 3 , p 4 ... are determined when p is 

 chosen. As we need a particular integral only of the equation for P' n , we may choose 

 p in any way that may be convenient. We shall put p = 0. Then 



, 



a ' 2.4(2n + 3) 



p = 



(52) 



To find the form of Q' H , we assume 



4 +-) (53) 



Then equations (50) and (38) give 



As before, ^ can be chosen arbitrarily, and then q a , q t> ... are known. We observe 

 that if we put 



9o = ' ft *-' '" f/a ' = -"" ^ 



the sequence equations for the q's are transformed into the sequence equations for the 

 p's, beginning with the equation containing p a , p t . We shall therefore choose q to 

 be (2n + 3)~ 1 2p 3 , and then 



->- 4 +...j . (54) 



2n+5 2n+7 



