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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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/840345 |
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| author | Dursun Tasci Mirac Cetin Firengiz Naim Tuglu |
| author_facet | Dursun Tasci Mirac Cetin Firengiz Naim Tuglu |
| author_sort | Dursun Tasci |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4c7171a0e97941308b2270a40b00e77f |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-4c7171a0e97941308b2270a40b00e77f2025-02-03T06:14:18ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/840345840345Incomplete Bivariate Fibonacci and Lucas 𝑝-PolynomialsDursun Tasci0Mirac Cetin Firengiz1Naim Tuglu2Department of Mathematics, Faculty of Science, Gazi University, Teknikokullar, 06500 Ankara, TurkeyDepartment of Mathematics, Faculty of Education, Başkent University, Baglica, 06810 Ankara, TurkeyDepartment of Mathematics, Faculty of Science, Gazi University, Teknikokullar, 06500 Ankara, TurkeyWe 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.http://dx.doi.org/10.1155/2012/840345 |
| spellingShingle | Dursun Tasci Mirac Cetin Firengiz Naim Tuglu Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials Discrete Dynamics in Nature and Society |
| title | Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials |
| title_full | Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials |
| title_fullStr | Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials |
| title_full_unstemmed | Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials |
| title_short | Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials |
| title_sort | incomplete bivariate fibonacci and lucas 𝑝 polynomials |
| url | http://dx.doi.org/10.1155/2012/840345 |
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