PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 943 
_(_ ot +) tae (4 sacha 
=(—c) io {1~ (= } 25 (7-1) rere. 1 

Let Bela Vegeta hn th 
€ =(5- ) agert mits en 
dy iiss 
dz dt} 
etl 
y=e (c+ a 2he—* ae ) 
wet 
Now er 1=0, except when p is a negative whole number; in which case 


y= Ceé ; except when yu is a negative whole number, in which case 
—p-1 geal 
sj) Ss. 
u-2  p=2 
Now, im all cases we omit the arbitrary functions in differentiation to any 
= w—l 
index ; they being readily supplied when required. But pra + &&., is evi- 
dently included in the arbitrary function, in the case in question ; we may there- 
fore omit it, and write generally, 
== Ces OF 
tes za new 
Se er il ci Gite s oaltdahchin cdl (4) 
This result has been deduced from the definition without any assumption 
whatever relative to the function |, except that it satisfies the condition /n+1=n/n. 
We may, consequently, obtain the value of the constant C, by admitting, that 
when n is positive, /n coincides with LrecEnpRE’s function /. In this case, 
[as “a e~“*q"—-ld a 
Po 0 ‘ 
Therefore, differentiating, to the index p, 
[n+ Me 
T+ be 

—Cfa“*"-1e-*"aa, by the definition and equation (1). 
x 
But if n+ be positive, /n + also coincides with Lecenpre’s function, there- 
fore, 
nN 
[O+ PB _ fj-aeqr+u-lda, or O=1. 
ela 

