Rit (Vísindafélag Íslendinga) - 01.06.1931, Page 23

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is a particular solution of any linear differential equation, we
select therefore, in (32) the lower limit of the integration
such that the integral becomes zero identically. On the other
hand, the higher limits have to satisfy the conditions speci-
fied below.
For the sake of brevity we shall only regard one term on
the right side of (32), from which we get:
dsy
dx5
= C,.
qVx rj* $ irj
(32a)
Further
»;s xp $ d)?
(32b)
A(risí))
= C, [xp-] | e’í*>;s>? \v — xp~2 [ e,,x
+ ...+(-1 yí'
+(—l)p-tx,-1| e”
d>;p_t
+ ...
„„ dvQfO)
d>;p
d>;]
Substituting from (32b) in (31), we get:
m
t=l p=t s=0
cpserx(—
p_t dp-t(>?5^)
d>;p_t
dp(ys&)
K ’ d>?p
d>; = 0
(31a)
From (31a) we infer that (32) is an integral of (31) if:
m n
S S <-»' c„ ^ = 0 (33)
P=0 s=0
m n
p=0 s=0
erx Cps ( l)p—‘
dp-f(>;s>9)
d>;p-‘
= 0
r\—v
(34)
for
t = 1, 2, 3 ... m.