28(5 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 



or ""(2 — ^) ^ + '^~'^^ J (~A — 6)5 + c 



= e'le ^^' ^ /(y + (y-%)+. ^^* ^ <^(y + (y-%)} 



These expressions do not appear to be susceptible of further reduction, ex- 

 cept in particular cases. 



Cor. Let 6=-r ; then 

 4 



To reduce this expression, it may perhaps be sufficiently general to suppose 

 the symbol 8h to include both the positive and negative signs, in which case we 



/-.. ^i 



may write only one of the functions «"'''^"'^"/(^+4^x). 



NoAV -^e "=/ due " . (See Gregory's jElcampfes, p. 499.) 



Let v= — = — ; then 



, / „ a - c or l \ 





and 



z = e'-' e-<''^''''^^f{y + ^x) 



^'K Jo •' V'' 4 4w / 



Section IV. Differences. 



22. The definition of the difference of ?/.,, as it is commonly written by 

 English authors is "a^+i — ":t. We shall retain this definition, and generalize it by 



d d 



writing e'^'^xi-x for «a:+i, and consequently (-■'' '-1) u,. for A'(,t. 



The results which we shall produce from this definition, as applied to firac- 



