1865.] Mr. W. H. L. Russell on Symbolical Expansions. 331 

 Hence we have generally, using II as a symbol for a continued product, 



whence the portion of (? + *)" which does not contain (TT) may he written 



&c. 



-72r-m+l 



the general term being A m) p r - m + 1 ^ 2r _ m+1 p; 



whence the part of the expansion of/(p-f TT), which does not contain TT, is 



+ &c. 

 If, then, we put 



we have 



+ &c., 

 the general term being 



A(m) 



where Ai. m) has the value given above ; and fi(x), / 2 (a;), /s(^), &c. are given 

 by the following formula, which, as I have before said, can be immediately 



VOL. XIV. 2 B 



