Rit (Vísindafélag Íslendinga) - 01.06.1946, Page 23

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The last expression is of a considerable importance because
it enables us to estimate the accuracy of the sum in question
and we can then proceed further in our calculations.
I wish further to have at hand a similar expression for
dy
----. This is readily accomplished by using (19) where I put
dt
p — 1. Hence:
^+_(k — n)[(kn — at2(\ +ecos(f + T))] — —~
t dy _________________________________ ,í! dt
dt k(k—1) + o^(l + e cos (í + t))
(38)
k- 1
n = 0
R = kt
i d i
(k — ri) [kn — at2(1 + ecos (/ + t))] — — + R
n\ dt
k (k — 1) + at~ (1 + e cos (t + x))
(*— 1)^-2 (+~) — + ecos(t + T)
(38a)
(y)
We notice that for a positive and |e| < 1 the denominator
in (37) and (38) does not vanish for any finite value of t
indepedant of k. Real poles for finite t are therefore excluded.
We are now able to write directiy down relations similar
to (37a) and (38a) reférring to the other end of our interval.
Then we have:
y0 =
(- t)n d"y
^T(k — n) (k — l + n)—-~—n+R
+-7, _______ iú dt
k (k — l) + at2 (1 + e cos x)
/ dy
(39)
R = k(k-l)R,_lA(y)-(k-\)lRk_2A
dt