Yazar "Akkus, Ilker" için listeleme
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A curious matrix-sum identity and certain finite sums identities
Kilic, Emrah; Akkus, Ilker; Omur, Nese; Ulutas, Yucel T. (World Scientific Publ Co Pte Ltd, 2015)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 ... -
Farey-Pell Sequence, Approximation To Irrationals And Hurwitz's Inequality
Akkus, Ilker; Irmak, Nurettin; Kizilaslan, Gonca (Int Center Scientific Research & Studies, 2016)The purpose of this paper is to give the notion of Farey-Pell sequence. We investigate some identities of the Farey-Pell sequence. Finally, a generalization of Farey-Pell sequence and an approximation to irrationals via ... -
The Fibonacci Octonions
Kecilioglu, Osman; Akkus, Ilker (Springer Basel Ag, 2015)In the present paper, we introduce the Fibonacci and Lucas octonions and give the generating function and Binet formulae for these octionions. In addition, we give some identities and properties of them. -
Formulas for binomial sums including powers of Fibonacci and Lucas numbers
Kilic, Emrah; Akkus, Ilker; Omur, Nese; Ulutas, Yucel Turker (Univ Politehnica Bucharest, Sci Bull, 2015)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. -
Generalization of a statistical matrix and its factorization
Akkus, Ilker; Kizilaslan, Gonca (Taylor & Francis Inc, 2019)We consider a special matrix with integer coefficients and obtain an LU factorization for its member by giving explicit closed-form formulae of the entries of L and U. Our result is applied to give the closed-form formula ... -
Generalized Binomial Convolution of the mth Powers of the Consecutive Integers with the General Fibonacci Sequence
Kilic, Emrah; Akkus, Ilker; Omur, Nese; Ulutas, Yucel T. (De Gruyter Open Ltd, 2016)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. -
The Lehmer matrix with recursive factorial entries
Akkus, Ilker (Academic Publication Council, 2015)A generalized Lehmer matrix with recursive entries from Kilic et al. (2010b) is further generalized, introducing three additional parameters and taking recursive factorials instead of a term. Certain formulae are derived ... -
The linear algebra of a Pascal-like matrix
Zheng, De-Yin; Akkus, Ilker; Kizilaslan, Gonca (TAYLOR & FRANCIS LTD, 2020)A Pascal-like matrix is constructed whose row entries are the terms of the modified Hermite polynomials of two variables. The multiplication of the two Pascal-like matrices and the power and inverse of the Pascal-like ... -
New Filbert and Lilbert matrices with asymmetric entries
Bozdag, Hacer; Kilic, Emrah; Akkus, Ilker (WALTER DE GRUYTER GMBH, 2020)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 ... -
On Fibonomial Sums Identities With Special Sign Functions: Analytically Q-Calculus Approach
Kilic, Emrah; Akkus, Ilker (Walter De Gruyter Gmbh, 2018)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. ... -
On some Properties of Tribonacci Quaternions
Akkus, Ilker; Kizilaslan, Gonca (Ovidius Univ Press, 2018)In this paper, we give some properties of the Tribonacci and Tribonacci-Lucas quaternions and obtain some identities for them. -
Partial sums of the Gaussian q-binomial coefficients, their reciprocals, square and squared reciprocals with applications
Kilic, Emrah; Akkus, Ilker (Univ Miskolc Inst Math, 2019)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 ... -
Quaternions: Quantum calculus approach with applications
Akkus, Ilker; Kizilaslan, Gonca (Academic Publication Council, 2019)In this paper we introduce two types of quaternion sequences with components including quantum integers. We also introduce quantum quaternion polynomials. Moreover, we give some properties and identities for these quantum ... -
Some Generalized Fibonomial Sums related with the Gaussian q-Binomial sums
Kilic, Emrah; Akkus, Ilker; Ohtsuka, Hideyuki (Soc Matematice Romania, 2012)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. -
Some New Quaternionic Quadratics with Zeros in Terms of Second Order Quaternion Recurrences
Akkus, Ilker; Kizilaslan, Gonca (Springer Basel Ag, 2019)In this paper a comprehensive analysis of the Horadam quaternion zeros for some new types of bivariate quadratic quaternion polynomial equations is presented. -
Split Fibonacci and Lucas Octonions
Akkus, Ilker; Kecilioglu, Osman (Springer Basel Ag, 2015)In this paper, split Fibonacci and Lucas octonions are proposed and their some properties and relations are obtained. -
A variant of the reciprocal super Catalan matrix
Kilic, Emrah; Akkus, Ilker; Kizilaslan, Gonca (De Gruyter Poland Sp Zoo, 2015)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 ...