- Kocaeli Journal of Science and Engineering
- Vol: 5 Issue: 2
- Unrestricted Pell and Pell – Lucas 2N-ons
Unrestricted Pell and Pell – Lucas 2N-ons
Authors : Öznur Bayrakçi Özsoy, Göksal Bilgici
Pages : 112-116
Doi:10.34088/kojose.1033409
View : 12 | Download : 8
Publication Date : 2022-11-30
Article Type : Research
Abstract :In this study, we define unrestricted Pell and Pell – Lucas hyper-complex numbers. We choose arbitrary Pell and Pell – Lucas numbers for the coefficients of the ordered basis 〖{e〗_0,e_1,⋯,e_(N-1)} of hyper-complex 2^N-ons where N∈{0,1,2,3,4} and call these hyper-complex numbers unrestricted Pell and Pell-Lucas 2N-ons. We give generating functions and Binet formulas for these type of hyper-complex numbers. We also obtain some generalization of well – known identities such as Catalan’s, Cassini’s and d’Ocagne’s identities.Keywords : Pell sequence, Pell-Lucas sequence, Quaternion, Octonion, Sedenion