V 



n=l 



453 



Sinmü___( — l)'^-ij*2A-l / 1 11 1 



712/" " (2A-1)/ " [l 



(1 + 1+1 + .. +^^^-- log,.) + 



(_l)».n2«+i 



4- V -a2/i-l-2n) 



Z- (2n + l)/ 



(7) 



and it is possible to express ti{2/i) by means of series of the form 



"=* smnw 

 V 



Indeed, putting 



>i=oe . mnv 



V,n = \ 2 and r = — 



o 



n=l ns 



we have by substituting in (4) 



i 



p =z 2. , Z := e 



I 



/) = 3 , z := e 



1 



2' 



1 ' 9.5-1 » 



whence 



^, + ^» - ^, = ï^. 



F. fl H ^ = 2 V, r,. 



M ~ Ss-l ƒ 1 9s— 1 * 



S-'-V ' 2* 



Now, talking s = 2h, we have ï^, :r= ri(2A), and expressing Fj 

 and F, by means of equation (7), we get an expansion for 'ii(2h). 

 In the simplest case h = l, I find in this way 



/ 4\ ':r" B„ t;2"+i /I A 



.(2) = i.(i + iogJ + i;^^--^-.-^(^-i) 



hi) 



Again the index of the series is -gV and the value of ')j(2) is found 

 to tive decimals by taking into account only the tirst two terms of 

 the expansion. 



