Greinar (Vísindafélag Íslendinga) - 01.01.1935, Page 109

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107
e-’*
The auxiliary equations8) belonging to (12) are:
Jl ds-qy , , , , xy- ds-q_1 y
X. 3s x + ^ /
s=q+l
as
s=q
dxs—q—1
=0, (13)
q=0,1,2,- ■ k.
From (13) we conclude tbat the limits of integration
are x=oo if ^ is positive, and x=o along with
dry 1
dxr
yx=o=0 and
Consequently we have:
f)=C I
=0 =0, r<k.
x=0
oo
-rjX
ydx
(14)
where y is derived from (12) or satisfies the equation
Zas
dsy
i=ö dxs
=C(
(15)
The constants c and ct in (14) and (15) are obviously
equal to 1, whence we conclude that y in (10) is the re-
quired solution of the differential equation (1)
It is not necessary that
k
Y. a* hs+1
s=0
is a linear function of q as might be supposed from (11).
It suffices that this function is capable of being expanded
into a power series of q.
Refurences.
0 JOHN R. CARSON, Electric Circuit Theory and the Opera-
tional Calculus, New York, 1926.
2) Carson, op. cit. p. 24.
3) Op cit p. 27.
4) Soc. Sci. Isl. XVII. Rvík. 1934.
5) Divergent Power Series, p. 23.
°) Op. cit. p. 23.
7) Cf. THORKELL THORKELSSON, Frequency Curves, Soc. Sci.
Isl. IX Rvik, 1931, pp. 24 and 27.
8) Cf. Frequency Curves pp. 25 & 33.
(Received Dec. 18th. 1935).