Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers

Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers

In 2007, Tachiya gave necessary and sufficient conditions for the transcendence of certain infinite products involving Fibonacci numbers F(k) and Lucas numbers L(k). In the present note, we explicitly evaluate two classes of his algebraic examples. Special cases are where phi = (1 + square root 5)/2...

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Bibliographische Detailangaben
1. Verfasser: Sondow, Jonathan
Format: Tagungsbericht
Sprache:eng
Schlagworte:
Algebra
Fibonacci numbers
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Beschreibung
Zusammenfassung:In 2007, Tachiya gave necessary and sufficient conditions for the transcendence of certain infinite products involving Fibonacci numbers F(k) and Lucas numbers L(k). In the present note, we explicitly evaluate two classes of his algebraic examples. Special cases are where phi = (1 + square root 5)/2 is the golden ratio.
ISSN:0094-243X
DOI:10.1063/1.3630044