Rit (Vísindafélag Íslendinga) - 01.06.1951, Page 76

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This is, however, not quite correct, the first equation being
more definite than the second one because of requiring not
only that the second relation between z and y subsists, but
also necessitating a defini:e relation between z (o) andy (o).
As to the first relation I Iike to point out in this connexion
that, when otherwise not expressively stated, it is involved
that n may be zero or any positive integer, in other words,
the remark n=o, 1,2,.... commonly added in these circum-
stances, is here omitted. The first equation refers to a
particular solution of the differential equation given by the
second equation.
We shall now look at a special case of (19) in that we
assume
uL=u, o.i—a-\ h, «3= a+2h, .... ar = a-f-(r—1 )h
Then we have
J' ■= a /„ x dxf xt~'dx S c;-5cx"~' dx
,s Ð k{zx-hs-'x)
ahs x
or
z= ahs(xh) *+ «/* Ðsh (x- °ý)
For h- o we get
and
dnz0 . sc.dnya
y=
Ðfnl(x--z)
(19a)
(18a)
in conformity with (21). We observe that in this case the
symbolic notation of (19a) gives
^ = — (00*. )-(*-«*)
a