Rit (Vísindafélag Íslendinga) - 01.06.1951, Side 88

88
[5]
From (36) we find
,((n±p)!\_ (-1)
A m
n\(n+q)!
L.J C ^_£)c,+m-p--lf.n+Pde
(q—p—i)/J o
(38)
where m is a positive, whole number. We obtain also from (36)
£jí / (n+rp) ! \ _1 r1 q—p—i
n[(n+q)!j~ (q~P~\)! J /
ln(l —e)
11
(1—E )n+Pd£
(39)
Before we proceed farther it is worth while to put to-
gether some useful formulae concerning the transformation
of the basal function, in order to emphasize their importance
although I have touched upon them above in connexion with
other problems.
From
dnz0 _ , , x dny0
~d^~ -<P(Ti + C0«)-^r
we get immediately the basal function
2==y(x(ld-A7?/o)))-Mp(ri)
or with regard to Az where I put a=1/a
z=^L «p(ii+«)
n = o
Hence, with reference to (40),
dnz0
ynl co
dny0
d(x' ‘T n!
__ / , \ dny0
d(xHo>)n — tpbl-F^ d(xiimy
and vice versa from
dnz0 , , ,dny0
dxn=<e('\+") dx.n
dnz0 , . x dny0
~o(^-^+am)-d&r
(40)
(40a)
(41)
(41 a)
We have shown, in Chapter 2, that we obtain from (40a)
dp z
dxn
= +P',=y'P',(x(l-|-A77/w)) q? (ti-}-co/z)