Rit (Vísindafélag Íslendinga) - 01.06.1946, Blaðsíða 14

14
The set of linear equations corresponding to (10) may now
be written
yi (r Ql(r + s t n)\( x)" / (n) (n) dpy \
ifb (r— t — n)\ (r + s — t)l n\ \ fr* x’p dxp I
= y s!(r+s~ f— n)! X í (n) , A(n) dPy0)
(s — rí)\(r+s —1)\n! V° £~0 °’p dx” )
+ K-tJy) (17)
t = 0, 1, 2...m — 1.
where the coefficients g{n\ g0l). A(n)p and A^p are given by
(14), (15) and (16) for n>m, while for n<m they are
zero excepting Aip)p = Aip)p = 1. Usually a more co.nve-
nient set of equations is that derived from (11) or
— r,! (rx -f- s — n)! (— x)n
n = 0 + — n)\ (r, -f s — t)\ n\
m—1
,(n + t) | X~ *(n + t)
' +
P = 0
p
dpy
dxp
S—t
(s — Q! (rt + s — t — rí) xn , (n + t)
(s — t— rí)\ (r, -|— s — t)! n\ )ff°
dfy )
m—1
dpy0
P = 0
A(n~\-t)___
°’p dxp
R
r,, s — t
dx*
(18)
where t — 0,1, 2...m — 1.
In (17) or (18) we have m linear equations between 2 m
quantities:
dy dfy_ dm~xy dy0 d'n~ly0
ff’ dx’ dx2 ’ dx,n~l ffo dx ’ dym~x
If m of them are known, the remaining m always may be
found provided the remainders are so small that they may