Incomplete Bivariate Fibonacci and Lucas p-Polynomials

We define the incomplete bivariate Fibonacci and Lucas p-polynomials. In the case x=1, y=1, we obtain the incomplete Fibonacci and Lucas p-numbers. If x=2, y=1, we have the incomplete Pell and Pell-Lucas p-numbers. On choosing x=1, y=2, we get the incomplete generalized Jacobsthal number and besides...

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Bibliographic Details
Published in:Discrete Dynamics in Nature and Society 2012-01, Vol.2012, p.1489-1499-198
Main Authors: Tasci, Dursun, Cetin Firengiz, Mirac, Tuglu, Naim
Format: Article
Language:English
Subjects:
Dynamics
Numbers
Studies
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Summary:We define the incomplete bivariate Fibonacci and Lucas p-polynomials. In the case x=1, y=1, we obtain the incomplete Fibonacci and Lucas p-numbers. If x=2, y=1, we have the incomplete Pell and Pell-Lucas p-numbers. On choosing x=1, y=2, we get the incomplete generalized Jacobsthal number and besides for p=1 the incomplete generalized Jacobsthal-Lucas numbers. In the case x=1, y=1, p=1, we have the incomplete Fibonacci and Lucas numbers. If x=1, y=1, p=1, k=⌊(n-1)/(p+1)⌋, we obtain the Fibonacci and Lucas numbers. Also generating function and properties of the incomplete bivariate Fibonacci and Lucas p-polynomials are given.
ISSN:1026-0226
1607-887X
DOI:10.1155/2012/840345