Generalized Cassini identities via the generalized Fibonacci fundamental system. Applications

I. M. Craveiro (), E. V. Pereira Spreafico () and M. Rachidi ()
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I. M. Craveiro: Mathematics Department - UFGD
E. V. Pereira Spreafico: INMA - UFMS
M. Rachidi: INMA - UFMS

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 4, 1234-1250

Abstract: Abstract In this paper we explore the generalized Cassini identities for the weighted generalized Fibonacci sequences, through the associated generalized Fibonacci fundamental system. Some algebraic, combinatoric and analytic properties of these identities are established. Applications to generalized Fibonacci and Pell numbers are provided, and some special cases are studied.

Keywords: Weighted generalized Fibonacci sequences; Generalized Cassini identities; Generalized Fibonacci Fundamental system; Combinatorial formulas; Analytical formulas; Generalized Fibonacci numbers; Generalized Pell numbers; Primary 11B39; 39A06; 39A60; Secondary 65Q10; 65Q30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00430-1

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