On a new generalization of split Pell quaternions

• Autorzy: Bród Dorota

Identyfikatory

DOI

10.14708/ma.v47i2.6510

Warianty tytułu

PL

O nowym uogólnieniu kokwaternionów Pella

• Języki publikacji: EN

Abstrakty

EN

In this paper we introduce and study a generalization of the split Pell quaternions - split r-Pell quaternions. We give some identities, among others Binet's formula, Catalan's, Cassini's and d'Ocagne's identity for these numbers.

PL

W artykule wprowadzono pewne jednoparametrowe uogólnienie kokwaternionów Pella - kokwaterniony r-Pella. Przedstawione zostały różne tożsamości dla tych liczb m.in. wzór Bineta, Catalana i Cassiniego.

Słowa kluczowe

EN

Pell numbers; quaternion; split quaternion; split Pell quaternion; split r-Pell quaternion

PL

liczby Pella; kwaternion; kokwaternion; kokwaternion Pella; kokwaternion r-Pella

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2019
• Tom: Vol. 47, no. 2
• Strony: 245--258
• Opis fizyczny: Bibliogr. 14 poz., fot., tab.

Twórcy

autor

Bród Dorota

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

Bibliografia

• [1] M. Akyiğit, H. Hüda Kösal, and M. Tosun. Split Fibonacci quaternions. Adv. Appl. Clifford Algebr., 23 (3):535-545, 2013. ISSN 0188-7009. doi: 10.1007/s00006-013-0401-9. MR 3093771. Cited on p. 248.
• [2] D. Bród. On a new one parameter generalization of Pell numbers. Ann. Math. Sil., 33 (1):66-76, 2019. ISSN 0860-2107. doi: 10.2478/amsil-2019-0011. Cited on pp. 247 and 248.
• [3] P. Catarino. On some identities and generating functions for k-pell numbers. Int. Journal of Math. Analysis, 7 (38):1877-1884, 2013. ISSN 1312-8876. doi: 10.12988/ijma.2013.35131. Cited on p. 247.
• [4] P. Catarino and P. Vasco. Some basic properties and a two-by-two matrix involving the k-pell numbers. Int. Journal of Math. Analysis, 7(45):2209-2215, 2013. ISSN 1312-8876. doi: 0.12988/ijma.2013.37172. Cited on p. 247.
• [5] J. Cockle. On systems of algebra involving more than one imaginary. Philosophical Magazine III, 35 (238):434-435, 1849. doi: 10.1080/02331880802264318. Cited on p. 245.
• [6] C. Flaut and V. Shpakivskyi. On generalized Fibonacci quaternions and Fibonacci-Narayana quaternions. Adv. Appl. Clifford Algebr., 23 (3):673-688, 2013. ISSN 0188-7009. doi: 10.1007/s00006-013-0388-2. Cited on p. 248.
• [7] S. Halici. On complex Fibonacci quaternions. Adv. Appl. Clifford Algebr., 23 (1):105-112, 2013. ISSN 0188-7009. doi: 10.1007/s00006-012-0337-5. Cited on p. 248.
• [8] A. Horadam. Complex fibonacci numbers and fibonacci quaternions. Amer. Math. Monthly, 70 (3):289-291, 1963. ISSN 0002-9890. doi: 10.1007/s00006-012-0337-5. Cited on p. 248.
• [9] A. Horadam. Pell identities. Fibonacci Quart., 9 (3):245-252, 1971. ISSN 0015-0517. doi: 10.1007/s00006-012-0337-5. Cited on p. 246.
• [10] E. Kocer and N. Tuglu. The binet formulas for the pell and pelllucas p-numbers. Ars Combin., 85 (1):3-17, 2007. ISSN 0381-7032. doi: 10.1007/s00006-012-0337-5. Cited on p. 247.
• [11] K. Piejko and I. Włoch. On k-distance pell numbers in 3-edge coloured graphs. J. Appl. Math, 2014 (1):6, 2014. ISSN 1110-757X. doi: 10.1155/2014/428020. Cited on p. 247.
• [12] E. Polatli, C. Kizilates, and S. Kesim. On split k-Fibonacci and k-Lucas quaternions. Adv. Appl. Clifford Algebr., 26 (1):353-362, 2016. ISSN 0188-7009. doi: 10.1007/s00006-015-0591-4. MR 3460005. Cited on p. 248.
• [13] U. Tokeşer, Z. Ünal, and G. Bilgici. Split Pell and Pell-Lucas quaternions. Adv. Appl. Clifford Algebr., 27 (2):1881-1893, 2017. ISSN 0188-7009. doi: 10.1007/s00006-016-0747-x. MR 3651547. Cited on p. 248.
• [14] Z. Ünal, U. Tokeşer, and G. Bilgici. Some properties of dual Fibonacci and dual Lucas octonions. Adv. Appl. Clifford Algebr., 27 (2):1907-1916, 2017. ISSN 0188-7009. doi: 10.1007/s00006-016-0724-4. MR 3651549. Cited on p. 248.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).