### 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 ∑′_{k ≥ 0} a^{k}/R_{cd(k)} + b′ 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.

Original language | English |
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Pages (from-to) | 115-128 |

Number of pages | 14 |

Journal | Monatshefte fur Mathematik |

Volume | 137 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2002 Oct 1 |

Externally published | Yes |

### Keywords

- Transcendence, Mahler functions

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Duverney, D., Kanoko, T., & Tanaka, T. A. (2002). Transcendence of certain reciprocal sums of linear recurrences.

*Monatshefte fur Mathematik*,*137*(2), 115-128. https://doi.org/10.1007/s00605-002-0501-4