某些Lucas级数的无理性

On the Irrationality of Certain Lucas Infinite Series

讨论Δ=p2-4q<0时的二元递推关系un+1=pun-qun-1(q≠0,q∈Z).设{un}与{vn}分别是初始11与∑∞进行某些情况下的求和与无理性的讨论.条件u0=0,u1=1与u0=2,u1=p下所得到的级数。

We consider the sequences of integers {un} defined by the recurrence relation un+1=pun-qun-1 (q≠0,q∈Z), and discuss the irrationality of ∑∞n=11un and ∑∞n=11vn in some conditions, where un and vn are the usual Lucas numbers.