564 
[554 
554. 
AN ELLIPTIC-TRANSCENDENT IDENTITY. 
[From the Messenger of Mathematics, vol. n. (1873), p. 179.] 
The following is a singular identity: 
(1 + q ) (1 + f) (1 + q 5 ) (1 + qj (1 + ? 9 ) • • • 
- (1 - q ) (1 - f) (1 - f) (1 - qj (1 - <f) • • • 
= 2q (1 + f) (1 + q 4 ) (1 + q 6 ) (1 + q s ) (1 + q 10 ) (1 + q 12 ) (1 + q 14 ) 2 (1 + q 16 ) 
where in each of the three terms every factor has the exponent 1 or 2 according as 
the exponent of q is not, or is, divisible by 7.