x_{n+b}=a_{n}+ c p^{n} x_{n} + u 


p^{k} (1p)^{nk} (x_{k}+x_{nk}), 
(n+1)ED_{n+1}=n+1 


p^{k} (1p)^{nk} (kED_{k}+(nk)ED_{nk}). 
(n+1)D_{n+1}(u)=1+u 


p^{k} (1p)^{nk} (kD_{k}(u)+(nk)D_{nk}(u)). 
(n+1)D_{n+1}(u)=1+u 


p 

··· p 

(k_{1}D 

(u)+...+k_{V} D 

(u)). 
(n+b)D_{n+b}(u)=b+u 


p^{k}(1p)^{nk}(kD_{k}(u)+(nk)D_{nk}(u)). 



D(z)=z+D(pz)+D(qz). 


(1)^{i}d(si)=(p^{s}+q^{s})d(s). 
d(s)= 



(1)^{i+1}d(si). 
D(z)= 

ó õ 

d(s)G(s) z^{s}ds 
D(z)= 

zlog z+ 
æ ç ç è 

+g 

ö ÷ ÷ ø 
z+zP_{1}(log z)+O(log z), 
b 
i 
d(s)= 

ó õ 

z^{s1} 

ED_{n} 

e^{z}dz= 



. 
d(s)= 


s(s+1)···(s+n1). 
X_{n}=1+q^{n}X_{n}+ 


p^{k}q^{nk}X_{k} 
L^{*}(s)= 

, 
L(z)= 

+ 

+ 

+P_{2}(log z)+O 
æ ç ç è 

ö ÷ ÷ ø 
. 
This document was translated from L^{A}T_{E}X by H^{E}V^{E}A.