72 A Generalisation of the Functions T (n) and x 



Let us form a function 

 0, ([*+!]) 



( 27 )- 



We notice that this function will reduce, factor by factor, to G (x), 



if we put/ = 1. 

 Difference Equatim. 



From the infinite product we have 



In the case (j?>l) the evaluation of the limit is not difficult, for 

 since 



r P ([ +i]) = [i] [2]... [4 



the expression 



so that 



0,(I* + l])-r,([*])0,([]) ............... (28). 



