1884.] K', E', J\ G' in powers of the modulus. 203 



By the change of q into q%, 



k' becomes ., -,- , 



I + tc 



§ 25. Starting with the formulae, 



ajri 12 12 02 12 02 K2 



v -i + 2 ^ + 2 *. 4" + 2 2 .4 S 



7T ■ 2^ 2 2 .4 fc 2 2 .4 2 .6 C " 



7T ~ 1 + 2 2 + 2 2 .4 2 + 2 2 .4 2 .6 2 + ' 



we find, by replacing &' by e~ 2i0 , and equating the real and 

 imaginary parts of the expressions as in § 23, 



14—2 



