Yazar "Kilic, Emrah" seçeneğine göre listele

Listeleniyor 1 - 9 / 9
  • Küçük Resim
    Öğe
    A curious matrix-sum identity and certain finite sums identities
    (World Scientific Publ Co Pte Ltd, 2015) Kilic, Emrah; Akkus, Ilker; Omur, Nese; Ulutas, Yucel T.
    In this paper, we consider two generalized binary sequences and then give a generalization of a matrix equality proposed as an advanced problem. Then, we derive new certain finite sums including the generalized binary sequences as applications.
  • [ X ]
    Öğe
    Diophantine Equations Related with Linear Binary Recurrences
    (Tarbiat Modares Univ, Acecr, 2022) Kilic, Emrah; Akkus, Ilker; Omur, Nese
    In this paper we find all solutions of four kinds of the Dio-phantine equations x(2) +/- V(t)xy - y(2) +/- x = 0 and x(2) +/- V(t)xy - y(2) +/- y = 0, for an odd number t, and, x(2) +/- V(t)xy + y(2) - x = 0 and x(2) +/- V(t)xy +/- y(2) - y = 0, for an even number t, where V-n is a generalized Lucas number. This paper continues and extends a previous work of Bahramian and Daghigh.
  • Küçük Resim
    Öğe
    Formulas for binomial sums including powers of Fibonacci and Lucas numbers
    (Univ Politehnica Bucharest, Sci Bull, 2015) Kilic, Emrah; Akkus, Ilker; Omur, Nese; Ulutas, Yucel Turker
    Recently Prodinger [2] proved general expansion formulas for sums of powers of Fibonacci and Lucas numbers. In this paper, we will prove general expansion formulas for binomial sums of powers of Fibonacci and Lucas numbers.
  • Küçük Resim
    Öğe
    Generalized Binomial Convolution of the mth Powers of the Consecutive Integers with the General Fibonacci Sequence
    (De Gruyter Open Ltd, 2016) Kilic, Emrah; Akkus, Ilker; Omur, Nese; Ulutas, Yucel T.
    In this paper, we consider Gauthier's generalized convolution and then define its binomial analogue as well as alternating binomial analogue. We formulate these convolutions and give some applications of them.
  • Küçük Resim
    Öğe
    New Filbert and Lilbert matrices with asymmetric entries
    (WALTER DE GRUYTER GMBH, 2020) Bozdag, Hacer; Kilic, Emrah; Akkus, Ilker
    In this paper, two new analogues of the Hilbert matrix with four-parameters have been introduced. Explicit formul ae are derived for the LU-decompositions and their inverses, and the inverse matrices of these analogue matrices. (C) 2020 Mathematical Institute Slovak Academy of Sciences
  • Küçük Resim
    Öğe
    On Fibonomial Sums Identities With Special Sign Functions: Analytically Q-Calculus Approach
    (Walter De Gruyter Gmbh, 2018) Kilic, Emrah; Akkus, Ilker
    Recently Marques and Trojovsky [On some new identities for the Fibonomial coefficients, Math. Slovaca 64 (2014), 809-818] presented interesting two sum identities including the Fibonomial coefficients and Fibonacci numbers. These sums are unusual as they include a rare sign function and their upper bounds are odd. In this paper, we give generalizations of these sums including the Gaussian q-binomial coefficients. We also derive analogue q-binomial sums whose upper bounds are even. Finally we give q-binomial sums formula whose weighted functions are different from the earlier ones. To prove the claimed results, we analytically use q-calculus. (C) 2018 Mathematical Institute Slovak Academy of Sciences
  • Küçük Resim
    Öğe
    Partial sums of the Gaussian q-binomial coefficients, their reciprocals, square and squared reciprocals with applications
    (Univ Miskolc Inst Math, 2019) Kilic, Emrah; Akkus, Ilker
    In this paper, we shall derive formulae for partial sums of the Gaussian q-binomial coefficients, their reciprocals, squares and squared reciprocals. To prove the claimed results, we use q-calculus. As applications of our results, we give some interesting generalized Fibonomial sums formulae.
  • Küçük Resim
    Öğe
    Some Generalized Fibonomial Sums related with the Gaussian q-Binomial sums
    (Soc Matematice Romania, 2012) Kilic, Emrah; Akkus, Ilker; Ohtsuka, Hideyuki
    In this paper, we consider some generalized Fibonomial sums formulae and then prove them by using the Cauchy binomial theorem and q-Zeilberger algorithm in Mathematica session.
  • Küçük Resim
    Öğe
    A variant of the reciprocal super Catalan matrix
    (De Gruyter Poland Sp Zoo, 2015) Kilic, Emrah; Akkus, Ilker; Kizilaslan, Gonca
    Recently Prodinger [8] considered the reciprocal super Catalan matrix and gave explicit formula for its LU-decomposition, the LU-decomposition of its inverse, and obtained some related matrices. For all results, q-analogues were also presented. In this paper, we define and study a variant of the reciprocal super Catalan matrix with two additional parameters. Explicit formula for its LU-decomposition, LU-decomposition of its inverse and the Cholesky decomposition are obtained. For all results, q-analogues are also presented.