Interesting interconnections between Hybrid Fibonacci and Lucas polynomials in two variable and golden ratio are worked out in the present paper. Inter connections are due to close relationship existing between hybrid Lucas and Fibonacci polynomials and the four kinds of Tchebyshev polynomials. In this way, the present paper provides a better interconnecting combinatorial picture of the golden ratio as well as hybrid Fibonacci and Lucas polynomials.
REFERENCES
1.
2.
W.
Gautschi
, Orthogonal Polynomials: Computation and Approximation,
Oxford University Press
, New York
, 2004
.3.
G. H.
Hardy
and E. M.
Wright
, An Introduction to Theory of Numbers,
Clarendon Press
, 1979
.4.
T.
Koshy
, Fibonacci and Lucas Numbers with Applications,
A Wiley Interscience Publication
, New York
, 2001
.5.
6.
J. C.
Mason
and D. C.
Handscomb
, Chebyshev Polynomials,
CRC Press LLC
, New York
, 2003
.7.
J.
Morgado
, Note on the Chebyshev Polynomials and Applications to the Fibonacci Number
, Portugaliae Mathematica,
52
(1995
), 363
–378
.8.
R.
Rangarajan
, Shashikala
P
and Honne
gowda C K
, Certain Combinatorial Identities of Twin Pairs Related to Tchebychev Polynomials
, International Journal of Computer Applications,
154
(05
) (2016
), 01
–05
.9.
R.
Rangarajan
, Shashikala
P
and Honne
gowda C K
, Certain Combinatorial Properties of Twin Triplets Related to Tchebychev Polynomials
, International Journal of Mathematics and its Applications
, 4
(4
) (2016
), 01
–10
.10.
R.
Rangarajan
, Honne
gowda C K
and Shashikala
P
, Certain Combinatorial Results on Two Variable Hybrid Fibonacci Polynomials
, International journal of computational and Applied Mathematics
, 12
(2
) (2017
), 603
–613
11.
R.
Rangarajan
, Honne
gowda C K
and Shashikala
P
, A Two Variable Lucas Polynomials Corresponding to Hybrid Fibonacci Polynomials
, Global Journal of pure and Applied mathematics,
12
(6
) (2017
), 1669
–1682
.12.
R.
Rangarajan
and P.
Shashikala
, A Pair of Classical Orthogonal Polynomials Connected to Catalan Numbers
, Adv Studies Contemp. Math.,
23
(2013
), 323
–335
.13.
J.
Riordan
, Combinatorial Identities,
Robert
E.
Krieger Publishing Company
, New York
, 1979
.14.
T.
Rivlin
, Chebyshev Polynomials: From Approximation Theory to Number Theory, Second edition,
Wiley and Sons
, New York
, 1990
.15.
Shashikala
P
and R.
Rangarajan
, Tchebychev and Brahmagupta Polynomials and Golden Ratio:Two New Interconnections
, International J. Math. Combin.,
3
(2016
), 57
–67
.16.
S.
Vajda
, Fibonacci and Lucas Numbers and Golden Section, Theory and Applications
, Ellis-Horwood
, London
, 1989
.
This content is only available via PDF.
©2023 Authors. Published by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.