( 73 ) 



12 



^(x{k) = o(^ve '''''' 'j 



we tind here out of (16) 



V 



where y denotes a certain positive constant ^). 

 Thus for e\^ery n we find 



Urn -^^— V f* (/"■) = (17) 



I— I 



§ 7. In ^ 5 I.e. we found out of 



km > II {k) = 



x=.(Xi <^ -^"^^ 



that the infinite series 



00 



converges for every pair of real values n, t; in the same way we 

 find out of (17): the infinite series 



' [i (k) logn k ,^-^ |Li {mb + h) log^ {mb + h) 



2w k^+ti ~ 2^ 



{mb + hy+ii 



k=l m=0 



converges for every pair of real values ?z, i. Here is proved in particular 

 for w = 0, ^ = the convergence supposed by Mr. Kluyver of the 

 infinite series 



00 



-^^ (I {mb -\- h) 

 ^^ mb-\-h 



TO— 



i. e. the existence of the quantity designated by him as Th,h' 



As now its existence is proved, it is easy to express its value in finite 



00 



form. As is known it follows from the convergence of "V" — , that 



^m^ n 



1) May be y—c-\- 1. 



