Year 2017, Volume , Issue 19, Pages 1 - 19 2017-11-01

A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL

A. D. Godase [1] , M. B. Dhakne [2]


The Fibonacci polynomial Fn(x) defined recurrently by Fn+1(x) = xFn(x)+Fn−1(x), with F0(x) = 0, F1(0) = 1, for n ≥ 1 is the topic of wide interest for many years. In this article, generalized Fibonacci polynomials Fbn+1(x) and Lbn+1(x) are introduced and defined by Fbn+1(x) = xFbn(x)+Fbn−1(x) with Fb0(x) = 0, Fb1(x) = x 2+4, for n ≥ 1 and Lbn+1(x) = xLbn(x)+Lbn−1(x) with Lb0(x) = 2x 2 + 8, Lb1(x) = x 3 + 4x, for n ≥ 1. Also some basic properties of these polynomials are obtained by matrix methods.
−Fibonacci Sequence, Fibonacci Polynomial, Generalised Fibonacci Polynomial
Other ID JA32GP55DV
Journal Section Research Article
Authors

Author: A. D. Godase

Author: M. B. Dhakne

Dates

Publication Date : November 1, 2017

Bibtex @ { jnt381418, journal = {Journal of New Theory}, issn = {2149-1402}, eissn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2017}, volume = {}, pages = {1 - 19}, doi = {}, title = {A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL}, key = {cite}, author = {Godase, A. D. and Dhakne, M. B.} }
APA Godase, A , Dhakne, M . (2017). A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL. Journal of New Theory , (19) , 1-19 . Retrieved from https://dergipark.org.tr/en/pub/jnt/issue/34520/381418
MLA Godase, A , Dhakne, M . "A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL". Journal of New Theory (2017 ): 1-19 <https://dergipark.org.tr/en/pub/jnt/issue/34520/381418>
Chicago Godase, A , Dhakne, M . "A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL". Journal of New Theory (2017 ): 1-19
RIS TY - JOUR T1 - A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL AU - A. D. Godase , M. B. Dhakne Y1 - 2017 PY - 2017 N1 - DO - T2 - Journal of New Theory JF - Journal JO - JOR SP - 1 EP - 19 VL - IS - 19 SN - 2149-1402-2149-1402 M3 - UR - Y2 - 2020 ER -
EndNote %0 Journal of New Theory A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL %A A. D. Godase , M. B. Dhakne %T A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL %D 2017 %J Journal of New Theory %P 2149-1402-2149-1402 %V %N 19 %R %U
ISNAD Godase, A. D. , Dhakne, M. B. . "A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL". Journal of New Theory / 19 (November 2017): 1-19 .
AMA Godase A , Dhakne M . A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL. JNT. 2017; (19): 1-19.
Vancouver Godase A , Dhakne M . A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL. Journal of New Theory. 2017; (19): 19-1.