Transcendence of Certain Reciprocal Sums of Linear Recurrences

 Suppose that {R _n } _n ⩾ 0 is a sequence of integers satisfying a binary linear recurrence relation with suitable conditions. We prove the transcendency of the numbers where a is a nonzero algebraic number and b, c, and d are integers with c ⩾ 1 and d ⩾ 2, and that of similarly constructed numbers, using a new theorem on the transcendence of functions.