hasan karatas - Academia.edu (original) (raw)
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University of the Basque Country, Euskal Herriko Unibertsitatea
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Papers by hasan karatas
Communications in Mathematics and Applications, 2019
In this study, we bring into light, a new generalization of the Jacobsthal Lucas numbers, which s... more In this study, we bring into light, a new generalization of the Jacobsthal Lucas numbers, which shall also be called the bi-periodic Jacobsthal Lucas sequence as Q n = 2bQ n−1 + Q n−2 , if n is even 2aQ n−1 + Q n−2 , if n is odd n ≥ 2, with initial conditions Q 0 = 2, Q 1 = a. The Binet formula as well as the generating function for this sequence are given. The convergence properties of the consecutive terms of this sequence are also examined after which the well known Cassini, Catalans and the D'Ocagne's identities as well as some related summation formulas are also given.
Communications in Mathematics and Applications, 2019
In this study, we bring into light, a new generalization of the Jacobsthal Lucas numbers, which s... more In this study, we bring into light, a new generalization of the Jacobsthal Lucas numbers, which shall also be called the bi-periodic Jacobsthal Lucas sequence as Q n = 2bQ n−1 + Q n−2 , if n is even 2aQ n−1 + Q n−2 , if n is odd n ≥ 2, with initial conditions Q 0 = 2, Q 1 = a. The Binet formula as well as the generating function for this sequence are given. The convergence properties of the consecutive terms of this sequence are also examined after which the well known Cassini, Catalans and the D'Ocagne's identities as well as some related summation formulas are also given.