Unrestricted pell and pell-lucas quaternions

Goksal Bilgici, Paula Catarino

Article ID: 816
Vol 4, Issue 1, 2021

VIEWS - 7048 (Abstract)

Abstract


In this study, we define the unrestricted Pell and Pell-Lucas quaternions. We give generating functions, Binet formulas and some generalizations of well-known identities such as Vajda’s, Catalan’s, Cassini’s d’Ocagne’s identities.


Keywords


Pell quaternion; Pell-Lucas quaternion; generating function

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References


. Catarino P. The Modified Pell and the Modified k-Pell Quaternions and Octonions. Advances in Applied Clifford Algebras 2016; 26(2): 577-590. . Çimen CB, İpek A. On Pell Quaternions and Pell-Lucas Quaternions. Advances in Applied Clifford Algebras 2016; 26(1): 39-51. . Horadam AF. Quaternion Recurrence Relations. Ulam Quarterly 1993; 2(2): 23-33. . Koshy T. Pell and Pell–Lucas Numbers with Applications. New York: Springer, 2014. . Szynal-Liana A, Wloch I. The Pell Quaternions and the Pell Octonions. Advances in Applied Clifford Algebras 2016; 26(1): 435-440. . Tokeşer Ü, Ünal Z, Bilgici G. Split Pell and Pell–Lucas Quaternions. Advances in Applied Clifford Algebras 2017; 27(2): 1881-1893.



DOI: https://doi.org/10.24294/ijmss.v1i3.816

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