Browsing by Author "Kizilates, Can"

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    q-Generalization of Biperiodic Fibonacci and Lucas Polynomials
    (2017) Kizilates, Can; Firengiz, Mirac Cetin; Tuglu, Naim; https://orcid.org/0000-0002-9588-0295; HNQ-9215-2023
    In this paper, we de fine q-analogue of the biperiodic Fibonacci and Lucas polynomials. We obtain generating function and several properties of these polynomials. We also define q-analogue of the biperiodic incomplete Fibonacci and Lucas polynomials. We show that these polynomials satisfy nonlinear recurrence relations. Then we prove several summation formulas for the biperiodic incomplete q-Fibonacci and q-Lucas polynomials
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    Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers
    (2021) Cetin, Mirac; Kizilates, Can; Yesil Baran, Fatma; Tuglu, Naim
    This paper is concerned with the combinatorial identities of the harmonic and the hyperharmonic Fibonacci numbers. By using the symmetric algorithm, we get some identities which improve the usual results and generalize known equations. Moreover, with the help of concept of Riordan array, we obtain the generating functions for these numbers and a variety of identities are derived