220 EXPANSION OF A FUNCTION 



., , 



therefore 



Similarly 



,. 

 hence /'(a) = A' 



which, for shortness, may be written 



/'M = *I+*' 



Similarly, 



/-(a) = * + unr 



The law of the formation of the successive differential 

 coefficients of /(a) is thus obvious. When a=0, /(a) be- 

 comes u ; hence we have 



Restore A for a/i, and ^ for aJc'; then, 



[2 



+ su> 



3 ( rfx 3 aara^ dxdy* 



