Reciprocal Sums of Second Order Recurrent Sequences
نویسندگان
چکیده
Let Z and IR (C) denote the ring of the integers and the field of real (complex) numbers, respectively. For a field F, we put i* = F\{0}. Fix A GC and B G C*, and let X(A, B) consist of all those second-order recurrent sequences {wn}neZ of complex numbers satisfying the recursion: n+i = „ ~ n-i (i.e., Bwn_Y = Awn wn+l) for n = 0, ± 1, ± 2,.... (1) For sequences in SE(A,B), the corresponding characteristic equation is x Ax + B-Q, whose roots {A ± ̂ A-4B) 12 are denoted by a and /?. If As R* and A = A 4B > 0, then we let A-*e(AhfK and p=A + sgorhfA (2) 2 r 2 w
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