CIRCUIT THF.OKV ./A/) OPF.RATIONAI. CALCULUS 7J'> 



Now »A|>,m(linn this liy tlu' MiKHiii.il llu'orrm 



= l+f, + ^V.... (86) 



/2a/ (2a/)' (2a/)» \ 



\ 1 "^ 1.:^ "^i.3.sT • ■/ 



1 



l>y till' usu.il Hi'a\isi(k' rules of "ali;fl)rizint;." 



It is worth while \erifyiiii; this from the iiitenral equation of the 

 problem. We luue 



1 1 /"° 



P \+\/a/p •'0 



The left hantl side i.in he written as 



(87) 



J 1_ la^ 



-a p-a\ p 



and 1)\- the formulas and theorems j;i\en in a preceding section the 

 solution can he recognized at once as: — 



^'^'^=^'-\l^'X'7T'^^ 



(88) 

 This ran also he written as 



If the definite integral of (88) is c\aluated by successive partial 

 integrations it will he found in agreement with the Heavisidc solution 

 (StV). 



Now the solution (86) is in powers of / and while absolutely con- 

 vergent becomes progressively more difficult to interpret and com- 

 [)ute as the value of / increases. From (80), however, we can derive 

 a divergent or asymptotic solution applicable both for interpreta- 

 tion and computation, when the value of / is sufficiently large. As 



