Some remarkable infinite product identities involving Fibonacci and Lucas numbers
Kunle Adegoke
TL;DR
This paper derives new infinite product identities involving Fibonacci and Lucas numbers by applying telescoping summation formulas to hyperbolic tangent identities with golden ratio powers.
Contribution
It introduces novel infinite product identities connecting Fibonacci and Lucas numbers using advanced summation techniques and properties of these sequences.
Findings
New infinite product identities involving Fibonacci and Lucas numbers
Application of telescoping summation formulas to hyperbolic tangent identities
Use of properties of the golden ratio in deriving identities
Abstract
By applying the classic telescoping summation formula and its variants to identities involving inverse hyperbolic tangent functions having inverse powers of the golden ratio as arguments and employing subtle properties of the Fibonacci and Lucas numbers, we derive interesting general infinite product identities involving these numbers.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Advanced Mathematical Identities · Mathematics and Applications