On a new generalization of Fibonacci hybrid numbers

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TAN E., Ait-Amrane N. R.

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, vol.54, no.2, pp.428-438, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1007/s13226-022-00264-3
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Page Numbers: pp.428-438
  • Keywords: Fibonacci sequence, Bi-periodic Horadam sequence, Horadam hybrid number, Hybrid number
  • Ankara University Affiliated: Yes


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 + cc + 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.