TY  - JOUR
T1  - Unrestricted Fibonacci and Lucas quaternions
AU  - Daşdemir, Ahmet
AU  - Bilgici, Göksal
PY  - 2021
DA  - March
Y2  - 2021
DO  - 10.33401/fujma.752758
JF  - Fundamental Journal of Mathematics and Applications
JO  - Fundam. J. Math. Appl.
PB  - Fuat USTA
WT  - DergiPark
SN  - 2645-8845
SP  - 1
EP  - 9
VL  - 4
IS  - 1
LA  - en
AB  - Many quaternion numbers associated with Fibonacci and Lucas numbers or even their generalizations have been defined and widely discussed so far. In all the studies, the coefficients of these quaternions have been selected from consecutive terms of these numbers. In this study, we define other generalizations for the usual Fibonacci and Lucas quaternions. We also present some properties, including the Binet's formulas and d'Ocagne's identities, for these types of quaternions.
KW  - Fibonacci quaternion
KW  - Lucas quaternion
KW  - Binet's formula
KW  - Catalan's identity
KW  - Generating function
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UR  - https://doi.org/10.33401/fujma.752758
L1  - https://dergipark.org.tr/en/download/article-file/1150737
ER  -