Incomplete Bivariate Fibonacci and Lucas ð ‘ -Polynomials

Dursun Tasci, Mirac Cetin Firengiz and Naim Tuglu

Discrete Dynamics in Nature and Society, 2012, vol. 2012, 1-11

Abstract:

We define the incomplete bivariate Fibonacci and Lucas ð ‘ - polynomials. In the case ð ‘¥ = 1 , 𠑦 = 1 , we obtain the incomplete Fibonacci and Lucas ð ‘ - numbers. If ð ‘¥ = 2 , 𠑦 = 1 , we have the incomplete Pell and Pell-Lucas ð ‘ - numbers. On choosing ð ‘¥ = 1 , 𠑦 = 2 , we get the incomplete generalized Jacobsthal number and besides for ð ‘ = 1 the incomplete generalized Jacobsthal-Lucas numbers. In the case ð ‘¥ = 1 , 𠑦 = 1 , ð ‘ = 1 , we have the incomplete Fibonacci and Lucas numbers. If ð ‘¥ = 1 , 𠑦 = 1 , ð ‘ = 1 , 𠑘 = ⌊ ( ð ‘› − 1 ) / ( ð ‘ + 1 ) ⌋ , we obtain the Fibonacci and Lucas numbers. Also generating function and properties of the incomplete bivariate Fibonacci and Lucas ð ‘ - polynomials are given.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:840345

DOI: 10.1155/2012/840345

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