Rit (Vísindafélag Íslendinga) - 01.06.1946, Page 19

19
Further
+ ,” + Tlr-rx
m + r— 1 x(r-l)
/o
dy x2 d2y
(28a)
and so on.
A similar procedure is also applicable with respect to
the asymptotic differentiation (19) and (20) as well as to
the solutions based upon it, cf. (23). Especially this method is
preferable, when the ordinary Maclaurin series has a great
tendency to divergence while the corresponding series ex-
panded from the other end (x = x) is more manageable:
(29)
ditional work is required to get from them the values of
dy dyQ
y, — etc. if y0,----, .... are known. Usually this is a draw-
dx dx
back. However, in some cases the additional work is quite
dx
minimal, mainly if some of the quantities y, —, etc. are
dy
zero.
The old method of solving differential equations by ex-
panding into a Maclaurin series is, of course, often the most
convenient solution. It should, however, be pointed out,
that the common belief that this method is restricted to