Simplicial $d$-Polytopic Numbers Defined on Generalized Fibonacci Polynomials
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913658640007168 |
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| author | López, Ronald Orozco |
| author_facet | López, Ronald Orozco |
| contents | In this article, we introduce the simplicial $d$-polytopic numbers defined on generalized Fibonacci polynomials. We establish basic identities and find $q$-identities known. Furthermore, we find generating functions for the simplicial $d$-polytopic numbers and for the squares of the generalized triangular numbers. Finally, we compute sums of reciprocals of generalized Fibonacci polynomials and generalized triangular numbers. Here we introduce the Zeta function defined on generalized Fibonacci polynomials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_11490 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simplicial $d$-Polytopic Numbers Defined on Generalized Fibonacci Polynomials López, Ronald Orozco Combinatorics Number Theory 11B39, 05A15, 11B65 In this article, we introduce the simplicial $d$-polytopic numbers defined on generalized Fibonacci polynomials. We establish basic identities and find $q$-identities known. Furthermore, we find generating functions for the simplicial $d$-polytopic numbers and for the squares of the generalized triangular numbers. Finally, we compute sums of reciprocals of generalized Fibonacci polynomials and generalized triangular numbers. Here we introduce the Zeta function defined on generalized Fibonacci polynomials. |
| title | Simplicial $d$-Polytopic Numbers Defined on Generalized Fibonacci Polynomials |
| topic | Combinatorics Number Theory 11B39, 05A15, 11B65 |
| url | https://arxiv.org/abs/2501.11490 |