On a new generalization of Fibonacci hybrid numbers
The hybrid numbers were introduced by Ozdemir [9] as a new generalization of complex, dual, and hyperbolic numbers. A hybrid number is defined by $k=a+bi+c\epsilon +dh$, where $a,b,c,d$ are real numbers and $% i,\epsilon ,h$ are operators such that $i^{2}=-1,\epsilon ^{2}=0,h^{2}=1$ and $ih=-hi=\eps...
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| Main Authors | , |
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| Format | Journal Article |
| Language | English |
| Published |
17.06.2020
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| Subjects | |
| Online Access | Get full text |
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| Summary: | The hybrid numbers were introduced by Ozdemir [9] as a new generalization of
complex, dual, and hyperbolic numbers. A hybrid number is defined by
$k=a+bi+c\epsilon +dh$, where $a,b,c,d$ are real numbers and $% i,\epsilon ,h$
are operators such that $i^{2}=-1,\epsilon ^{2}=0,h^{2}=1$ and $ih=-hi=\epsilon
+i$. This work is intended as an attempt to introduce the bi-periodic Horadam
hybrid numbers which generalize the classical Horadam hybrid numbers. We give
the generating function, the Binet formula, and some basic properties of these
new hybrid numbers. Also, we investigate some relationships between generalized
bi-periodic Fibonacci hybrid numbers and generalized bi-periodic\ Lucas hybrid
numbers. |
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| DOI: | 10.48550/arxiv.2006.09727 |