Rit (Vísindafélag Íslendinga) - 01.06.1951, Síða 106

[5]
106
(g+£)x2
4
Cx 1-
1+A0 i ux
+ ^“(l+Ao)-
(1+Ao)2
(1+ ^ 0 + Ao)
b-\-4a
2a
í
n y2 \ö+^a
■ Ckll + ^-d + ^Ur-*
(o—V2)/
1 V.
(0-V2)/ (0+V2)/
+
flX'*
Ö+6
2 \(o+V*)/ 2c (0+V2)//
&+■<«
ríi i öJCVi Í * \\- "tf' í o ax* 2a(o+2) +é\
=c, 1+-2-o+a„) * - fc+is>+T • ■ 2æ+wr
Ci
flX3
ö+ía
(l +Ao) 2a
(0+1/.)/
, fl^ L . ax* , A
+ 1-(1 + ^(l+Ao))
\ i+*L o + 2 + Ó+ö
2a
(o+«/*)/
=0
We observe that the nth term of the A\- series of the latest
written basal function is offset by the (fl+l)f/i term of the
preceding series, while the first term of this series is zero.
We have considered the factor C of the precedent^solu-
tions as constant and, therefore, independent of n which is
correct so long as n is a whole number. However, it is
frequently convenient to drop this characteristic of n Now
if we change n to fl+a where a is an intermediary quantity
between o and 1, C may assume a new value that remains
constant as long as n is a whole number. It is tempting
to change n to /Z+V2 in (65), we must, however, remember
that C, at the same time, gets a new value.
In what follows we shall replace C by K when we wish
to indicate that K represents an arbitrary functiou of n with
period 1. If the period is 2 we write K<2> and so on. Re-
caliing that C in (65) actually should be K the introduc-
tion of /í+Va for n entails a new value on C.
We have, therefore,