Generating Functions For Two-Variable Polynomials Related To a Family of Fibonacci Type Polynomials and Numbers

被引：21

作者：

Ozdemir, Gulsah ^{[1
]}

Simsek, Yilmaz ^{[1
]}

机构：

[1] Akdeniz Univ, Fac Sci, Dept Math, TR-07058 Antalya, Turkey

来源：

FILOMAT | 2016年 / 30卷 / 04期

关键词：

Fibonacci numbers; Fibonacci polynomials; Jacobsthal polynomials; Chebyshev polynomials; Vieta-Fibonacci polynomials; Vieta-Lucas polynomials; Humbert polynomials; Geganbauer polynomials; generating functions;

D O I：

10.2298/FIL1604969O

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to construct generating functions for the family of the Fibonacci and Jacobsthal polynomials. Using these generating functions and their functional equations, we investigate some properties of these polynomials. We also give relationships between the Fibonacci, Jacobsthal, Chebyshev polynomials and the other well known polynomials. Finally, we give some infinite series applications related to these polynomials and their generating functions.

引用

页码：969 / 975

页数：7

共 12 条

[1]

[Anonymous], 2005, ADV STUD CONT MATH

[2]

[Anonymous], 1984, A Treatise on Generating Functions

[3]

Djordjevic G. B., 2006, J INDONESIAN MATH SO, V12, P99

[4] Incomplete generalized Jacobsthal and Jacobsthal-Lucas numbers [J].

Djordjevic, GB ;

Srivastava, HM .

MATHEMATICAL AND COMPUTER MODELLING, 2005, 42 (9-10) :1049-1056

[5] POLYNOMIALS RELATED TO GENERALIZED CHEBYSHEV POLYNOMIALS [J].

Djordjevic, Gospava B. .

FILOMAT, 2009, 23 (03) :279-290

[6] On k-Fibonacci sequences and polynomials and their derivatives [J].

Falcon, Sergio ;

Plaza, Angel .

CHAOS SOLITONS & FRACTALS, 2009, 39 (03) :1005-1019

[7]

Horadam AF, 2002, FIBONACCI QUART, V40, P223

[8]

KOSHY T., 2001, PUR AP M-WI

[9]

Mezo I, 2009, J INTEGER SEQ, V12

[10] Sums of powers of Fibonacci polynomials [J].

Prodinger, Helmut .

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2009, 119 (05) :567-570

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