OF THE FORM &?. 397 



0-* (q+p)l(2n-2r)\(n + q-r)\ 



^-* r (q-p)\ r\ (q-r)l (n-r}\ (2n + 2q-2r+l)\ 



(n-m-)! 

 where s takes all values from to q p. 



Simplifying these expressions we see that 



-r)\ (2q-2r)l (n + m) 



rl(q-r)l(n-r)l(2n + 2q-2r 





, p-, (n-m + q+p-2r)l 



>l+ "- 2r 



and also that 



fv / _ i y (n + m + 2q 2r s) ! (n m + s) \ 1 

 ' 6' ! (q -p - s) I (n - m - 2r + s) I (n + m-s) \\ 



-m + 2g-2r-s)! 



s ! ( q -p - ,) \ (,;+ m - 2r + .9) ! (n - m - s) ! ' 



15. From the relation between the functions Q and H, as given in 

 Section I. (p. 248), we get 



Qm+v = 1.3 .5...(2n + 2g_- 4r - 1) p 



V n+5 -2r _ +-2r 



and 



' 4r)! jjm-p 



n+q-2r 



