Rit (Vísindafélag Íslendinga) - 01.06.1946, Page 10

1Ó
<!,) “ r'+<-fe)+F+'Ifr+r+ij (i
tsjc

^V\
(r + s)2[(r + S)2-l] \ dx2 )
which for r = s becomes
<?y
R.Q/)=R.+i(y)-
X
4 (4 s2 — 1)

dx
(12c)
(12d)
When writing down our set of equations we must evi-
dently avoid such equations that according to (12a) and
(12b) are a consequence of -those already written down.
The solutions (10) or (11) include the ordinary solution by
means of Maclaurin series, (r = 0), but although this series
fails to give practical solution on account of divergence
of the series, the equations (10) and (11) are still usable,
dr-+*+V
provided that —is finite in the interval concerned
dx + +1
and
dr+3+1y(&x)
d(dx)r-+s+1
&r’ (1 —&Y * is small at the ends (for
= 0 and i? = 1).
The computation of the coefficients
r!(r+s — n)! 1 s!(r + s — n)! 1
——------------- = — and ------------------= (13)
(r—n)!(r+s)!n! «n (s —n)! (r + s) n! |3n
is readily carried out. However, I find it more practical to
take them from tables. I have, therefore, in Table I (page
12) put down the most usual values of an and (3n.