41 



II 



\2 .. r>s dS ^ ' n+l n n ^ ..2^ .. , „2ns ns f^ 



('^^ i)'^p„%iP;+-^^ —^(1 - /^^)^ + ^^p„%i Pn'r—2 



da dn ^ \^ 



.(n+l)(p- ^Ik^^ps 1^\(1-m') ^M 



A |(n + l)(n + s + 1)(P„^2 + (n + l)(n - s + l)(P„%i)= 



[117] 



+ 2[s2 - (n + 1) 





/i 2(n + s + 1)! 

 ,2 (n - s)! 



using [104] and [106]. This integration breaks down when s = 0, because s appears in the 

 denominators of [104] and [106], but the result is still valid. The reduced form of the inte- 

 gral for s = becomes 



(n + l)2j \^ipy , ipo^^ )2 ^2^po poj^ 



1-/.2 



in + 1)2 r [(^P^"- p;^^)2 , (pO)2 (1 _ ^2)] _± 

 J -1 I - 



r 1 r(l - M^) 19 

 J_iL (« + i) 



dy. 



1-Z.2 



by [98]. Using [102], this reduces to 2{n + 1). 



INTEGRALS //s, s±i) 



These integrals, which were needed to evaluate F, and P, , were defined as 



o ; 1 y Iz ' 



IJs, s±l) = r |p„^^jP^=^i[(l-^2)(^^l)2+s(s ±i)+(n+l)(2s±l)] 



+ (r 



+ _:L±i ^I!__ (1 



dp. dp 



