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$d-$Fibonacci and $d-$Lucas polynomials | ||
| Journal of Mathematical Modeling | ||
| مقاله 7، دوره 9، شماره 3، آذر 2021، صفحه 425-436 اصل مقاله (304.49 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2021.17837.1538 | ||
| نویسندگان | ||
| Boualem Sadaoui1؛ Ali Krelifa* 2 | ||
| 1LESI Laboratory, Faculty of Sciences and Technology, University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana, 44225 Algeria | ||
| 2LESI Laboratory, Faculty of Sciences and Technology, University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana 44225, Algeria | ||
| چکیده | ||
| Riordan arrays give us an intuitive method of solving combinatorial problems. They also help to apprehend number patterns and to prove many theorems. In this paper, we consider the Pascal matrix, define a new generalization of Fibonacci and Lucas polynomials called $d-$Fibonacci and $d-$Lucas polynomials (respectively) and provide their properties. Combinatorial identities are obtained for the defined polynomials and by using Riordan method we get factorizations of Pascal matrix involving $d-$Fibonacci polynomials. | ||
| کلیدواژه‌ها | ||
| $d-$Fibonacci polynomials؛ $d-$Lucas polynomials؛ Riordan arrays؛ Pascal matrix؛ $Q_{d}-$Fibonacci matrix | ||
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