Abstract.
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.
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Received February 8, 2001; in final form April 4, 2002
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Duverney, D., Kanoko, T. & Tanaka, Ta. Transcendence of Certain Reciprocal Sums of Linear Recurrences. Monatsh. Math. 137, 115–128 (2002). https://doi.org/10.1007/s00605-002-0501-4
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DOI: https://doi.org/10.1007/s00605-002-0501-4