scholarly journals Generating Functions of Modified Pell Numbers and Bivariate Complex Fibonacci Polynomials

2019 ◽  
Vol 7 (4) ◽  
pp. 113-116
Author(s):  
Souhila Boughaba ◽  
Ali Boussayoud ◽  
Khadidja Boubellouta
Keyword(s):  
Generating Functions ◽  
Fibonacci Polynomials ◽  
Pell Numbers

scholarly journals Construction of a new class of generating functions of binary products of some special numbers and polynomials

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 1001-1013
Author(s):  
Souhila Boughaba ◽  
Ali Boussayoud ◽  
Serkan Araci ◽  
Mohamed Kerada ◽  
Mehmet Acikgoz
Keyword(s):  
Chebyshev Polynomials ◽  
Generating Functions ◽  
Fibonacci Numbers ◽  
Fibonacci Polynomials ◽  
Pell Numbers ◽  
New Class ◽  
Special Numbers And Polynomials ◽  
Symmetric Properties

In this paper, we derive some new symmetric properties of k-Fibonacci numbers by making use of symmetrizing operator. We also give some new generating functions for the products of some special numbers such as k-Fibonacci numbers, k-Pell numbers, Jacobsthal numbers, Fibonacci polynomials and Chebyshev polynomials.

scholarly journals Symmetric functions of the k-Fibonacci and k-Lucas numbers

2020 ◽  
pp. 2150031
Author(s):  
Ali Boussayoud ◽  
Mohamed Kerada ◽  
Serkan Araci ◽  
Mehmet Acikgoz
Keyword(s):  
Generating Functions ◽  
Symmetric Functions ◽  
Lucas Numbers ◽  
Fibonacci Polynomials ◽  
Pell Numbers ◽  
Symmetric Properties

In this paper, we introduce a new operator in order to derive some new symmetric properties of [Formula: see text]-Fibonacci and [Formula: see text]-Lucas numbers and Fibonacci polynomials. By making use of the new operator defined in this paper, we give some new generating functions for [Formula: see text]-Fibonacci and Pell numbers and Fibonacci polynomials.

scholarly journals Some Properties of the(p,q)-Fibonacci and(p,q)-Lucas Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
GwangYeon Lee ◽  
Mustafa Asci
Keyword(s):  
Generating Functions ◽  
Combinatorial Identities ◽  
Fibonacci Polynomials ◽  
Lucas Polynomials ◽  
Pascal Matrix ◽  
Riordan Arrays ◽  
Combinatorial Sums

Riordan arrays are useful for solving the combinatorial sums by the help of generating functions. Many theorems can be easily proved by Riordan arrays. In this paper we consider the Pascal matrix and define a new generalization of Fibonacci polynomials called(p,q)-Fibonacci polynomials. We obtain combinatorial identities and by using Riordan method we get factorizations of Pascal matrix involving(p,q)-Fibonacci polynomials.

scholarly journals Symmetric and generating functions of generalized (p,q)-numbers

2021 ◽  
Vol 48 (4) ◽  
Author(s):  
Nabiha Saba ◽  
◽  
Ali Boussayoud ◽  
Abdelhamid Abderrezzak ◽  
◽  
...  
Keyword(s):  
Generating Functions ◽  
Fibonacci Numbers ◽  
Lucas Numbers ◽  
Pell Numbers ◽  
Lucas Polynomials ◽  
Binet’S Formula

In this paper, we will firstly define a new generalization of numbers (p, q) and then derive the appropriate Binet's formula and generating functions concerning (p,q)-Fibonacci numbers, (p,q)- Lucas numbers, (p,q)-Pell numbers, (p,q)-Pell Lucas numbers, (p,q)-Jacobsthal numbers and (p,q)-Jacobsthal Lucas numbers. Also, some useful generating functions are provided for the products of (p,q)-numbers with bivariate complex Fibonacci and Lucas polynomials.

scholarly journals On Generalized Third-Order Pell Numbers

2019 ◽  
pp. 1-18
Author(s):  
Yüksel Soykan
Keyword(s):  
Generating Functions ◽  
Third Order ◽  
Pell Numbers ◽  
Summation Formulas ◽  
Special Cases

In this paper, we investigate the generalized third order Pell sequences and we deal with, in detail, three special cases which we call them third order Pell, third order Pell-Lucas and modified third order Pell sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

scholarly journals Summing a Family of Generalized Pell Numbers

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Helmut Prodinger
Keyword(s):  
Linear Combination ◽  
Computer Algebra ◽  
Generating Functions ◽  
Fibonacci Numbers ◽  
Partial Sums ◽  
Pell Numbers ◽  
New Family ◽  
Binet Formula

AbstractA new family of generalized Pell numbers was recently introduced and studied by Bród ([2]). These numbers possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of generalized Pell numbers can be summed explicitly. For this, as a first step, a power P lnis expressed as a linear combination of Pmn. The summation of such expressions is then manageable using generating functions. Since the new family contains a parameter R = 2r, the relevant manipulations are quite involved, and computer algebra produced huge expressions that where not trivial to handle at times.

scholarly journals Properties of hyperbolic generalized Pell numbers

2020 ◽  
Vol 26 (4) ◽  
pp. 136-153
Author(s):  
Yüksel Soykan ◽  
◽  
Melih Göcen ◽  
Keyword(s):  
Clifford Algebra ◽  
Generating Functions ◽  
Hyperbolic Numbers ◽  
Lucas Numbers ◽  
Pell Numbers ◽  
Summation Formulas ◽  
Special Cases

In this paper, we introduce the generalized hyperbolic Pell numbers over the bidimensional Clifford algebra of hyperbolic numbers. As special cases, we deal with hyperbolic Pell and hyperbolic Pell–Lucas numbers. We present Binet’s formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan’s, Cassini’s, d’Ocagne’s, Gelin–Cesàro’s, Melham’s identities and present matrices related to these sequences.

scholarly journals ORDINARY GENERATING FUNCTIONS OF BINARY PRODUCTS OF (p,q)-MODIFIED PELL NUMBERS AND k-NUMBERS AT POSITIVE AND NEGATIVE INDICES

2020 ◽  
Vol 20 (3) ◽  
pp. 627-648
Author(s):  
NABIHA SABA ◽  
ALI BOUSSAYOUD
Keyword(s):  
Generating Functions ◽  
Lucas Numbers ◽  
Pell Numbers ◽  
Balancing Numbers ◽  
Symmetric Properties

In this paper, we introduce a operator in order to derive some new symmetric properties of (p,q)-modified Pell numbers and we give some new generating functions of the products of (p,q)-modified Pell numbers with k-Fibonacci and k-Lucas numbers, k-Pell and k-Pell Lucas numbers, k-Jacobsthal and k-Jacobsthal Lucas numbers at positive and negative indices. By making use of the operator defined in this paper, we give some new generating functions of the products of (p,q)-modified Pell numbers with k-balancing and k-Lucas-balancing numbers.

scholarly journals GENERATING FUNCTIONS OF EVEN AND ODD GAUSSIAN NUMBERS AND POLYNOMIALS

2021 ◽  
Vol 21 (1) ◽  
pp. 125-144
Author(s):  
NABIHA SABA ◽  
ALI BOUSSAYOUD ◽  
MOHAMED KERADA
Keyword(s):  
Generating Functions ◽  
Symmetric Functions ◽  
Fibonacci Numbers ◽  
Lucas Numbers ◽  
Pell Numbers ◽  
New Class ◽  
Gaussian Polynomials

In this study, we introduce a new class of generating functions of odd and even Gaussian (p,q)-Fibonacci numbers, Gaussian (p,q)-Lucas numbers, Gaussian (p,q)-Pell numbers, Gaussian (p,q)-Pell Lucas numbers, Gaussian Jacobsthal numbers and Gaussian Jacobsthal Lucas numbers and we will recover the new generating functions of some Gaussian polynomials at odd and even terms. The technique used her is based on the theory of the so called symmetric functions.

Sign in / Sign up

Export Citation Format

Share Document