Abstract
In this paper, by using q-integers and higher-order generalized Fibonacci numbers, we define the higher-order generalized Fibonacci quaternions with q-integer components. We give some special cases of these newly established quaternions. This article examines q-calculus and quaternions together. We obtain a Binet-like formula, some new identities, a generating function, a recurrence relation, an exponential generating function, and sum properties of quaternions with quantum integer coefficients. In addition, we obtain some new identities for these types of quaternions by using three new special matrices.
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Kapsamı
Uluslararası
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Type
Hakemli
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Index info
WOS.SCI
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Language
English
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Article Type
None
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Keywords
<italic>q</italic>-calculus Binet formula <italic>q</italic>-integer recurrence relation Fibonacci quaternions higher-order generalized Fibonacci numbers higher-order generalized Fibonacci quaternions with <italic>q</italic>-integer components