Unrestricted pell and pell-lucas quaternions

Goksal Bilgici ,Paula Catarino

doi:10.24294/ijmss.v1i3.816

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Unrestricted pell and pell-lucas quaternions

Goksal Bilgici

Paula Catarino

International Journal of Mathematics and Systems Science 2021, 4(1); https://doi.org/10.24294/ijmss.v1i3.816

Submitted：09 May 2018

Accepted：24 May 2018

Published：03 Dec 2021

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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.

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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.

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