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On Bicomplex ( p,q )-Fibonacci Quaternions

Author

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  • Çağla Çelemoğlu

    (Department of Mathematics, Faculty of Science, Ondokuz Mayıs University, Samsun 55270, Turkey)

Abstract

Here, we describe the bicomplex p , q -Fibonacci numbers and the bicomplex p , q -Fibonacci quaternions based on these numbers to show that bicomplex numbers are not defined the same as bicomplex quaternions. Then, we give some of their equations, including the Binet formula, generating function, Catalan, Cassini, and d’Ocagne’s identities, and summation formulas for both. We also create a matrix for bicomplex p , q -Fibonacci quaternions, and we obtain the determinant of a special matrix that gives the terms of that quaternion. With this study, we get a general form of the second-order bicomplex number sequences and the second-order bicomplex quaternions. In addition, we show that these two concepts, defined as the same in many studies, are different.

Suggested Citation

  • Çağla Çelemoğlu, 2024. "On Bicomplex ( p,q )-Fibonacci Quaternions," Mathematics, MDPI, vol. 12(3), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:461-:d:1330449
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    References listed on IDEAS

    as
    1. Can Kızılateş & Paula Catarino & Naim Tuğlu, 2019. "On the Bicomplex Generalized Tribonacci Quaternions," Mathematics, MDPI, vol. 7(1), pages 1-8, January.
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