182 
On Expansions in Tetracliorie Functions 
TABLE VI. 
dx, 1/ = - 1-3010412, p = 4, q = ^, m = 5i*. 
s 
as 
Tetrachoric 
Functions 
Terms in 
Series - a^Tg 
Value of Series 
up to terms t. 
0 
1 -00000000 
-0966212 
-0966212 
-0966212 
3 
- ■28327885 
+ -04839695 
+ •0137098 
■1103310 
4 
- -01400852 
+ -05941568 
+ -0008323 
-1111633 
5 
+ -16688842 
- -06703628 
+ •0111876 
•1223509 
6 
+ -05349154 
- -00778490 
+ -0004164 
•1227673 
7 
- -05325140 
+ -05554783 
+ -0029580 
•1257253 
8 
- -09445982 
- -01930950 
- -0018240 
•1239013 
9 
- -00063525 
- -03745046 
- -0000238 
•1238775 
True value -1188790. 
TABLE VIL 
B(4, f) 
- dx, 2/ = - 3-59087385t. 
Tetrachoric 
Terms in 
Value of Series 
s 
Functions Tj 
Series - a^rg 
up to term 
0 
1 -00000000 
-0001648 
-0001648 
•0001648 
3 
- -28327885 
+ -00307042 
+ -0008698 
-0010346 
4 
- -01400852 
- -00458580 
- -0000642 
•0009704 
5 
+ -16688842 
+ -00530458 
-- -0008853 
■0000851 
6 
+ 05349154 
- -00442734 
+ -0002368 
•0003219 
7 
- -05325140 
+ -00191632 
+ -0001020 
■0004239 
8 
- -09445982 
+ -00111687 
+ -0001055 
■0005294 
9 
- -00063525 
- -00291 774 
- -0000019 
•0005275 
True value -00023603. 
5th or 6th tena as at the 15th, say, and better than at the 30th. Of course, one 
might calculate the various terms till the sums became more or less steady, take 
the mean of these sums after the steady stage is reached and use that as the value 
required. This process, however, will not give a greater accuracy than three or four 
decimal places correct and very likely the result will not be so good as that. Besides 
which it is difficult to give such an arbitrary weighting of terms a theoretical 
justification. Thus it seems that the tetrachoric series is not at all suitable for the 
representation of the Licomplete F-function. 
P 
p + q 
•17408520 
-= - 1-30104] 2. 
P 
ti/ = _-lii= /J 1^ --3-59087385. 
a •17408o2b 
