# Binomials transformation formulae for scaled Fibonacci numbers

Edyta Hetmaniok; Bożena Piątek; Roman Wituła

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 477-485
- ISSN: 2391-5455

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topEdyta Hetmaniok, Bożena Piątek, and Roman Wituła. "Binomials transformation formulae for scaled Fibonacci numbers." Open Mathematics 15.1 (2017): 477-485. <http://eudml.org/doc/288113>.

@article{EdytaHetmaniok2017,

abstract = {The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.},

author = {Edyta Hetmaniok, Bożena Piątek, Roman Wituła},

journal = {Open Mathematics},

keywords = {δ-Fibonacci numbers; δ-Lucas numbers; Binomial transformation; -Fibonacci numbers; -Lucas numbers; binomial transformation},

language = {eng},

number = {1},

pages = {477-485},

title = {Binomials transformation formulae for scaled Fibonacci numbers},

url = {http://eudml.org/doc/288113},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Edyta Hetmaniok

AU - Bożena Piątek

AU - Roman Wituła

TI - Binomials transformation formulae for scaled Fibonacci numbers

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 477

EP - 485

AB - The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.

LA - eng

KW - δ-Fibonacci numbers; δ-Lucas numbers; Binomial transformation; -Fibonacci numbers; -Lucas numbers; binomial transformation

UR - http://eudml.org/doc/288113

ER -

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