Infinite Series Involving Fibonacci Numbers Via Ap\'ery-Like Formulae
Chance Sanford
TL;DR
This paper derives infinite series involving Fibonacci and Lucas numbers using Apéry-like formulae, providing new mathematical identities inspired by Apéry's approach to zeta function irrationality.
Contribution
It introduces novel infinite series involving Fibonacci and Lucas numbers based on Apéry-like techniques, expanding the toolkit for studying special number sequences.
Findings
Derived new infinite series involving Fibonacci numbers
Established identities connecting Fibonacci and Lucas numbers
Applied Apéry-like methods to sequence-based series
Abstract
In this note, infinite series involving Fibonacci and Lucas numbers are derived by employing formulae similar to that which Roger Ap\'ery utilized in his seminal paper proving the irrationality of .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Advanced Mathematical Identities · Mathematics and Applications