1904.] A Generalisation of the Functions F(n) and x a . -. 71 

 Certain series of interest in connection with the function F are _ 



r, ([*+]) 



[su + w 





dx T p ([x]) 





\ !og^ 

 ' J(P^~ 



(P-l) 



(25). 



[][+!] . . . [x + n-l] 





C n = ,- 





In case^ = 1, the series (25) is . . 



a_j,a(a-l) 1 a 

 x * a; (a; + 1) ' a; 



9. The Function G p ([x]). A function 



G (x) - L 



n=cc 



with the properties 



l (a -2) 



is given in Whittaker's Modern Analysis, p. 201, and is there referred 

 to Alexeiewsky. This function has been discussed in detail in a more 

 general form by E. W. Barnes.* From (26) we obtain without 

 difficulty 



= L 



* ' Lond. Math. Soc. Proc.,' vol. 31, pp. 358 et seq. 



