THE HEAVISIDE OPERATIONAL CALCULUS 55 



On the basis of tlie preceding and with the aid of fornuihi (10), 

 expansions of the type 



!//)//(/)) ~ -i- ^bn/P" + ' = f^ e~''h{l)dt 

 which occur in physical problems, can be dealt with. For since 



^ h„/p- + ^ = n dt e-f' V b„t-/n\ 

 and 



it follows from (10) that 



V TT ^0 v/ — y ^^ 



1 ^p hn{2tY 



^/—t 2^ (2« - 1) (2n - 3) . . r 



