124 Mr Mordell, On Mr Ramanujan's Empirical Expansions, etc. 

 where /le (?i) is defined* by 



1 



= r [(1 + r)(l-r2)(l +rO(l -r^) . ..]'/[(! -r"){l-7^){\-r') ...]«. 



Mr Ramanujan overlooks the fact that Cy = ^fu{p)- 

 These results can be proved by aid of the principles used in 

 finding equations (3) and (4). We should however have to consider 

 now invariants of a sub-group of the modular group, and it seems 

 hardly worth while to go into details. 



* The functions /lo ('O'/ieC**) arise in finding the number of representations of 

 n as a sum of 10 and 16 squares respectively and the series 2 S [x + njY r* "^^^ is 

 well known in this connection. 



