1879.] the Values of the Theta and Zeta Functions. 355 

 § 4. Also, squaring the values in the last group, 



e^iK+^KO = q~t— &W*{cos \Q + i sin &c., 



so that we have the following table : — 



u. 







fK+f*K' 



7T 



- 2 -t { (i + V) * + i (i - &o *} 



7T 



q-l—m* { (1 - * + i(l + V)*} 



7T 



(1 - &') * - t(l + A?')*} 



(i-k'y-i(i + //)^} 



7T 



and, squaring again, 









fK + fiK' 



q-&^kW*(k' + ik) 



7T 2 



q-^kW^k'+ik) 



q-¥Rtfk\-k'-+ik) 



q-*—m\-k r -ik) 

 9TT2 



q-l—m f t(-k'-ik) 



7T 2 

 7T 2 



§ 5. In the case of the Z function, we have 



z(iK) =j(i-r), 



Z(iK+JtK') = -i^+i(i+«'), 



