512 
A MEMOIR ON THE SINGLE AND DOUBLE THETA-FUNCTIONS. 
[704 
© Oi li 
00 
10 
01 
11 
Of If (2m) = I J 
0 
1 
2 
3 
K L 
The functions of (2u') are denoted in like manner by accented letters 
© 
00 
00 
(2 u') = X', 
&c., 
© li 
22 
00“ 
10 
01 
11 
if if ft (% u ) — 4/ N P 
0 “ 
1 
2 
3 
Q 
85. To simplify the expression of the results, instead of in each case writing 
down the suffixes, I have indicated them by means of the column headed “ Suff.” 
Thus 
Suff. 
| 8-0 | u+ u'= XX' + YY' + ZZ' + WW' \ 2 1 
means that the equation is to be read 
= ij; + f 2 f/ + + w,w'. 
It is hardly necessary to mention that the | 8 — 0 of the left-hand column shows 
the current numbers of the theta-functions; viz. the left-hand side of the equation is 
(u + u). Sq (u — u'). 
And by a preceding remark the single arguments u + v! and u — u' are written in 
place of (u + u', v + v') and (u — u', v — v') respectively.