Yazar "Kilic, Emrah" için listeleme
-
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 ... -
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. -
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. -
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. ... -
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 ... -
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. -
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 ...