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Transcendency Results for Sums of Reciprocals of Linear Recurrences
Author(s) -
Becker PaulGeorg,
Töpper Thomas
Publication year - 1994
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19941680102
Subject(s) - mathematics , transcendental number , integer (computer science) , sequence (biology) , binary number , lucas sequence , combinatorics , rational number , transcendental equation , discrete mathematics , arithmetic , mathematical analysis , classical orthogonal polynomials , numerical analysis , biology , computer science , genetics , programming language , fibonacci polynomials , orthogonal polynomials
Suppose that { R n } n ≥0 is a linear recursive sequence and d ≥ 2 is an integer. Under suitable conditions on { R n } and d we show that\documentclass{article}\pagestyle{empty}\begin{document}$$ \sum\limits_{h = 0}^\infty {\frac{1}{{R_{d^h } }}} $$\end{document}and similarly constructed numbers are transcendental. Special attention is given to the case of binary recurrences.