PROFESSOR KELLAND ON A PROCESS 


| ee fixe 
Hence ea ax) "log 2= = — =i NEO ee =, 8 
5 pr | TeP am fit@ 
F io 
al 
u 1 
a) 
rm =| 
=r 7 ii 
[ro™ 
9. To sind the differential equation, on the solution of which depends the value 

r 1 1 
{oe Gane tees haut Ta 



of d* e®*. 
Since a1 +art+ eS + be. 
/=i-arie f=247 p 
deem (ante tas! a i — 5 as | 
[~r Lo # 
This equation can be made to depend on the solution of a differential equa- 
tion, when 7 is a whole number ; for, in that case, the terms will recur after the 
rth. To reduce the equation, we observe that 




[=@+1)+rp j=l+rp 
r ay eee | ne 4 
ere aera TEE , and so on. 
anne [7 
eta er et 






Hence 
Swen 
island 2 
[Te ck pp ag tot +? 
Ae Be) (75 uae jr+2 + Ger) + bey des Joo. A) 
Lak ae 
rpr+l—r 
Ae i ee ao ab 
Let YT Lag (Bab Gate t= ae 
aetg2ttl-re (r+1) (2r+1) 
; : 
ort (pei ee beucstars ; then 
ey eg 2 ae eel 
god, =a" ia sae 
Si a lt petestorn)**} 
Ci heey 
(=r it [=@+2)+rp 
aru! %. ce malls I, is & 
jr+2 [_r+2- i 
ae 
Again, if I=T5 =) 
2 = 

