×

On Pell quaternions and Pell-Lucas quaternions. (English) Zbl 1344.11022

Summary: The main object of this paper is to present a systematic investigation of new classes of quaternion numbers associated with the familiar Pell and Pell-Lucas numbers. The various results obtained here for these classes of quaternion numbers include recurrence relations, summation formulas and Binet’s formulas.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
05A15 Exact enumeration problems, generating functions
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Akyigit, M.; Kösal, H.H.; Tosun, M., Split Fibonacci quaternions, Adv. Appl. Clifford Algebr., 23, 535-545, (2013) · Zbl 1328.11016
[2] Cerin, Z.; Gianella, G.M., On sums of pell numbers, Acc. Sc. Torino-Atti Sc. Fis., 141, 23-31, (2007)
[3] Cerin, Z., Gianella, G.M.: On sums of squares of Pell-Lucas numbers. Integers Electron. J. Comb. Number Theory 6, #A15,1-16 (2006) · Zbl 1094.11009
[4] Everest, G., Ward, T.: An introduction to number theory. In: Graduate Texts in Mathematics, Springer, London (2005) · Zbl 1089.11001
[5] Filipponi, P.; Horadam, A.F., Real pell and pell-Lucas numbers with real subscripts, Fibonacci Quart., 33, 5, (1995) · Zbl 0838.11012
[6] Flaut, C.; Shpakivskyi, V., On generalized Fibonacci quaternions and Fibonacci-Narayana quaternions, Adv. Appl. Clifford Algebr., 23, 673-688, (2013) · Zbl 1330.11009
[7] Güren, I.A., Nurkan, S.K.: A new approach to Fibonacci, Lucas numbers and dual vectors. Adv. Appl. Clifford Algebr. doi:10.1007/s00006-014-0516-7 · Zbl 0838.11012
[8] Gürlebeck, K., Sprössig, W.: Quaternionic and Clifford Calculus for Physicists and Engineers. Wiley, New York (1997) · Zbl 0897.30023
[9] Halici, S., On Fibonacci quaternions, Adv. Appl. Clifford Algebr., 22, 321-327, (2012) · Zbl 1329.11016
[10] Halici, S., On complex Fibonacci quaternions, Adv. Appl. Clifford Algebr., 23, 105-112, (2013) · Zbl 1270.11012
[11] Hoggatt, V.E.: Fibonacci and Lucas numbers. In: A publication of the Fibonacci Association. University of Santa Clara, Santa Clara. Houghton Mifflin Company (1969) · Zbl 0198.36903
[12] Horadam, A.F., Complex Fibonacci numbers and Fibonacci quaternions, Am. Math. Mon., 70, 289-291, (1963) · Zbl 0122.29402
[13] Horadam, A.F., Pell identities, Fibonacci Quart., 9, 245252, (1971) · Zbl 0219.10018
[14] Horadam, A.F., Quaternion recurrence relations, Ulam Quart., 2, 23-33, (1993) · Zbl 0846.11013
[15] Iyer, M.R., A note on Fibonacci quaternions, Fibonacci Quart., 3, 225-229, (1969) · Zbl 0191.32701
[16] Koshy, T.: Fibonacci and Lucas numbers with applications. Wiley-Intersection, New York (2001) · Zbl 0984.11010
[17] Niederreiter, H., Spanier, J. (eds.): Monte Carlo and Quasi-Monte Carlo Methods, vol. 1998. Springer, Berlin (2000) · Zbl 0924.00041
[18] Nurkan, S.K., Güren, I.A.: Dual Fibonacci quaternions. Adv. Appl. Clifford Algeb. doi:10.1007/s00006-014-0488-7
[19] Swamy, M.N.S., On generalized Fibonacci quaternions, Fibonacci Quat., 11, 547-549, (1973) · Zbl 0281.10006
[20] Vajda, S.: Fibonacci and Lucas numbers and the Golden section. Ellis Horwood Limited Publ., England (1989) · Zbl 0695.10001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.