journal-of-information-and-optimization-sciences Journal of Information and Optimization Sciences 2169-0103 0252-2667 Taru Publications 10.47974/JIOS-1400 Balancing and Lucas-Balancing hybrid numbers and some identities Uysal Mine Graduate School of Natural and Applied Sciences, Erzincan Binali Yıldırım University, Erzincan, 24100, Türkiye Özkan Engin Department of Mathematics, Faculty of Sciences, Marmara University, İstanbul, 34722, Türkiye 45 5 1293 1304 12 08 2024

In this paper, we introduce Balancing and Lucas-Balancing hybrid numbers. We examine some identities of Balancing and Lucas-Balancing hybrid numbers. We give some basic definitions and properties related to them. In addition, we find Binet’s Formula, Cassini’s identity, Catalan’s identity, d’Ocagne identity, generating functions, exponential generating functions of the Balancing and Lucas-Balancing hybrid numbers.

 Balancing hybrid numbers Lucas-Balancing numbers Binet’s Formula Cassini’s identity Catalan’s identity access open retracted no