474 
TABLES OF THE DEVELOPMENTS OF FUNCTIONS &C. 
[216 
and, for the convenience of reference, I here give it as far as e 7 , viz., 
/= g + 2 [sin] 4 sin ig, 
where, as in the other sine series, i is to be taken as well negatively as positively, 
and [sin]" 4 = — [sin] 4 . Or, what is the same thing, 
f=g + % [sin] 4 2 sin ig, 
where i has only positive values. And the coefficients are 
e e 2 
e 3 
e 4 
e 5 
e 6 
<4 
[sin] 1 = I 
l 
~ 8 
+ 
192 
107 
9216 
[sin] 2 = +| 
11 
" 48 
+ -H 
3 8 4 
[sin] 3 ■ 
!3 
+ — 
24 
43 
128 
+ 95 
1024 
[sin] 4 = 
+ 103 
192 
_ 451 
960 
[sin] 5 = 
+ io 97 
1920 
_ 5957 
9216 
[sin] 6 = 
+ 1223 
1920 
[sin] 7 = 
+ 47273 
645 12 
The expression for -, as far as e 13 , is given in Schubert’s work, above referred 
CL 
to; and that of log (^j, as far as e 9 , was calculated by Oriani, see the Introduction 
to Delambre’s Tables clu Soleil, Paris, 1806.