A study of harmonic Fibonacci polynomials associated With Bernoulli-F and Euler–Fibonacci polynomials

Naim Tuglu (), Semra Kuş () and Can Kızılateş ()
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Naim Tuglu: University of Gazi
Semra Kuş: University of Kırşehir Ahi Evran
Can Kızılateş: University of Zonguldak Bulent Ecevit

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 4, 1129-1141

Abstract: Abstract In this paper, by the help the F-vacuum operator, we define the harmonic Fibonacci polynomials and harmonic based F-exponential generating function. The harmonic based F-exponential generating function is obtained for the Bernoulli-F polynomials, the Euler-Fibonacci numbers, the Euler-Fibonacci polynomials and the Bernoulli-Fibonacci numbers, and their relations are shown with the harmonic Fibonacci numbers and polynomials.

Keywords: Harmonic Fibonacci number; Umbral method; Special polynomial; Exponential generating function; 11B37; 05A40; 33C52 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00413-2

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