Bernoulli-Fibonacci Polynomials
Oktay K. Pashaev, Merve Ozvatan
TL;DR
This paper introduces Bernoulli-Fibonacci polynomials using Golden derivatives and exponential functions, exploring their properties and relations to Fibonacci numbers and the Golden ratio.
Contribution
It presents a novel class of Bernoulli-Fibonacci polynomials defined via Golden derivatives and explores their properties and connections to Fibonacci numbers.
Findings
Derived generating functions for Bernoulli-Fibonacci polynomials
Established properties paralleling classical Bernoulli polynomials
Connected Fibonacci numbers and Golden ratio to polynomial formulas
Abstract
By using definition of Golden derivative, corresponding Golden exponential function and Fibonomial coefficients, we introduce generating functions for Bernoulli-Fibonacci polynomials and related numbers. Properties of these polynomials and numbers are studied in parallel with usual Bernoulli counterparts. Fibonacci numbers and Golden ratio are intrinsically involved in formulas obtained.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Mathematical Theories and Applications · Advanced Combinatorial Mathematics