Browsing by Author "Firengiz, Mirac Cetin"

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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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    SHIFTED EULER-SEIDEL MATRICES
    (2017) Firengiz, Mirac Cetin; Dil, Ayhan
    In this study defining Shifted Euler-Seidel matrices we generalize the Euler-Seidel matrices method. Owing to this generalization one can investigate any sequences. (s(n)) which have two term linear recurrences as s(m+n) = alpha s(m+n-1) + beta s(n-1) (alpha and beta are real parameters and n, m is an element of Z(+)). By way of illustration, we give some examples related to the Fibonacci p-numbers.