Binomials transformation formulae of scaled Lucas numbers

• Autorzy: Wituła, R.
• Języki publikacji: EN

Abstrakty

EN

The current paper represents a suplement for papers [7] and [8]. Many of the new summation formulae connecting Lucas numbers with binomials are presented here. All these relations are obtained by using definition and simple properties of the so called δ-Lucas numbers.

Słowa kluczowe

PL

liczby Fibonacciego; liczby Lucasa; transformacja dwumianów

EN

δ-Fibonacci numbers; δ-Lucas numbers; binomials transformation

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 1
• Strony: 15--27
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Wituła, R.

• Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland,

Bibliografia

• [1] A. T. Benjamin, J. J. Quin, Proofs That Really Count - the Art of Combinatorial Proof, Mathematical Association of America, 2003.
• [2] P. Filipponi, Some binomial and Fibonacci identities, Fibonacci Quart. 33(3) (1995), 251–257.
• [3] R. A. Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific Publishing, 2006.
• [4] M. A. Khan, H. Kwong, Some binomial identities associated with the generalized natural number sequence, Fibonacci Quart. 49(1) (2011), 57–65.
• [5] T. Koshy, Fibonacci and Lucas Numbers with Application, Wiley, New York, 2001.
• [6] S. Vajda, Fibonacci and Lucas numbers and the Golden Section: Theory and Applications, Dover Press, 2008.
• [7] R. Wituła, Binomials transformation formulae of scaled Fibonacci numbers, Fibonacci Quart. (in review).
• [8] R. Wituła, D. Słota, δ-Fibonacci numbers, Appl. Anal. Discrete Math. 3 (2009), 310–329.