Browsing by Author "Tuglu, Naim"

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    On The Q - Seidel Matrix
    (2014) Firengiz, M. Cetin; Tuglu, Naim; https://orcid.org/0000-0002-9588-0295; HNQ-9215-2023
    Clarke and et. al recently introduced the q-Seidel matrix, and obtained some properties. In this article, we define a different form of q-Seidel matrix by a(n)(k) (x, q) = xq(n+2k-3)a(n)(k-1) (x, q)+an(k-1)(x, q)+a(n+1)(k-1) with k >= 1, n >= 0 for an initial sequence a(n)(0) (x, q) = a(n) (x, q). By using our definition, we obtain several properties of the q-analogues of generalized Fibonacci and Lucas polynomials.
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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 for Fibonacci and Incomplete Fibonacci p-Numbers via the Symmetric Matrix Method
    (2014) Firengiz, M. Cetin; Tasci, Dursun; Tuglu, Naim; 0000-0002-9588-0295; HNQ-9215-2023
    We obtain some new formulas for the Fibonacci and Lucas p-numbers, by using the symmetric infinite matrix method. We also give some results for the Fibonacci and Lucas p-numbers by means of the binomial inverse pairing.
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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
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    SOME RESULTS ON THE q-ANALOGUES OF THE INCOMPLETE FIBONACCI AND LUCAS POLYNOMIALS
    (2019) Srivastava, H.M.; Tuglu, Naim; Cetin, Mirac
    In the present paper, we introduce new families of the q-Fibonacci and q-Lucas polynomials, which are represented here as the incomplete q-Fibonacci polynomials F-n(k) (x, s, q) and the incomplete q-Lucas polynomials L-n(k) (x, s, q), respectively. These polynomials provide the q-analogues of the incomplete Fibonacci and Lucas numbers. We give several properties and generating functions of each of these families q-polynomials. We also point out the fact that the results for the q-analogues which we consider in this article for 0 < q < 1 can easily be translated into the corresponding results for the (p, q)-analogues (with 0 < q < p <= 1) by applying some obvious parametric variations, the additional parameter p being redundant.