Rit (Vísindafélag Íslendinga) - 01.06.1931, Side 5

5
rect integration of the right side of (3) is not possible:
nevertheless, determination of the constants of the frequency
curves in question is obtainable by means of the semi-invari-
ants. I shall here only outline a procedure that in every case
will serve the purpose:
Let the frequency curve be given by the differential
equation (2) and our object be to determine ao, ai, 32, ...
bo, bi, b2 ... etc., from the semi-invariants ^i, h, h, h ...
We prefer writing (3) in an abbreviated form:
rX2
$ = ev = / e"x y dx (3a)
J Xt
By repeated differentiation of (3a) with regard to y we
obtain the following relations:
d<?
d v
d2 0
d>f
dnd
d>jn
x y dx.
x2 y dx.
x” y dx
•' Xl
(6)
Further, multiplying (3a) with >] and integrating the right
side by parts, we get:
V # =
(7)
in that we only concern ourselves with cases where ye"11 is
zero at the limits x = xi and x = X2.
From (7) it follows that:
dW
d V
x dy.
J Xi
dn(>j&)
d >jn
(8)