On Pell and Pell-Lucas Hybrid Numbers

• Autorzy: Szynal-Liana A. , Włoch I.

Identyfikatory

DOI

10.14708/cm.v58i1-2.6364

• Języki publikacji: EN

Abstrakty

EN

In this paper we introduce the Pell and Pell-Lucas hybrid numbers as special kinds of hybrid numbers. We describe some properties of Pell hybrid numbers and Pell-Lucas hybrid numbers among other we give the Binet formula, the character and the generating function for these numbers.

Słowa kluczowe

EN

Pell numbers; recurrence relations; complex numbers; hyperbolic numbers; dual numbers

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2018
• Tom: Vol. 58, No. 1/2
• Strony: 11--17
• Opis fizyczny: Bibliogr. 8 poz., tab.

Twórcy

autor

Szynal-Liana A.

• Rzeszow University of Technology, Faculty of Mathematics and Applied Physics, Powstańców Warszawy 12, 35-959 Rzeszów, Poland

autor

Włoch I.

• Rzeszow University of Technology, Faculty of Mathematics and Applied Physics, Powstańców Warszawy 12, 35-959 Rzeszów, Poland

Bibliografia

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• [2] P. Catarino and P. Vasco, Modified k-Pell sequence: some identities and ordinary generating function, Appl. Math. Sci. 121 (2013), 6031-6037, DOI 10.12988/ams.2013.39513.
• [3] P. Catarino and P. Vasco, Some basic properties and a two-by-two matrix involving the k-Pell numbers, Int. J. Math. Anal. (Ruse) 45 (2013), 2209-2215, DOI 10.12988/ijma.2013.37172.
• [4] A. Dasdemir, On the Pell, Pell-Lucas and modified Pell numbers by matrix method, Appl. Math. Sci. 64 (2011), 3173-3181.
• [5] A. F. Horadam, Minmax Sequences for Pell Numbers, Applications of Fibonacci Numbers, Vol. 6, 1996, 231-249, DOI 10.1007/978-94-009-0223-7_19.
• [6] A. F. Horadam, Pell identities, Fibonacci Quart. 9 (1971), no. 3, 245-263.
• [7] M. Özdemir, Introduction to Hybrid Numbers, Adv. Appl. Clifford Algebr. 28 (2018), 11, DOI 10.1007/s00006-018-0833-3.
• [8] A. Szynal-Liana, The Horadam Hybrid Numbers, Discuss. Math. Gen. Algebra Appl. 38 (2018), 91-98, DOI 10.7151/dmgaa.1287.