OF TWO LEGENDRE'S COEFFICIENTS. 369 



23. If now we put 1*. = ^, and if we put 



2 cos <i = x + - and 2 cos md> = x m + 

 x x 



the value of Q n becomes 



The value of Q n may also be put under the form 



4. p p ' + 



~ - 1 >t - 1 ' 



If now we put 1* = ^, the value of Q n becomes 



/7~" P d n P 1 r/" m P rl m P i 



n / __ 1 \" " ' 4. I / _ i\m a ^n " ^n - 



; cT" d*" x" 1 ; d*- m d. m x m 



24. When ^ = ^, 



and V= I - 2h [> + 1 - ^) cos <^] -f 



= {(1 -A) 2 + 2/i(l -/A 2 )(l -cos 

 A. IT. 47 



