The path length of random skip lists - Institut für Analysis und ...

Proof. Immediate. D
Now we are ready to express [zn -1 ]H(z) as a complex contour integral . We confine
ourselves here to show how the method works for two of the seven terms in (2 .6) .
Let us start with the relatively simple first one, namely
A 1 (z) _ ( 1 z )
With the substitution z = w"' I we have
and therefore
From Lemma 3 (2 .18) we find
Therefore, by Lemma 2,
Here we have
where
A 7 (z)
1 A7
1 -w Cw- 1/
i>1
i
:
Qq12
=
( l I
Z)2 A1(z) .
1 _ l -w
Qi] 1 - wgti
1 1wA1Cww 1) =-
[zn-1 ]A1(z) = 2i 1 B(n + 2, -z) Q Z 2 21 dz . (2 .24)
(1 -
w l E S