Analysis of the Distribution and Asymptotic Approximations of Roots of the Polynomial Equation $$ z^{n+1}=(1+z)^n, n \in \mathbb{N} $$ in the Complex Plane
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909748558823424 |
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| author | Yadeta, Hailu Bikila |
| author_facet | Yadeta, Hailu Bikila |
| contents | We study the spatial distribution of the positive, negative and non-real complex roots $z_n $ of the sequence the $(n+1)$th degree polynomial equation $$ z^{n+1}=(1+z)^n,\quad n \in \mathbb{N}.$$
We establish asymptotic approximations to the sequence of the negative, the positive and the non-real complex roots of the equation as $n\rightarrow \infty $.
In addition, we discuses the possible areas of applications of the current problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15818 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of the Distribution and Asymptotic Approximations of Roots of the Polynomial Equation $$ z^{n+1}=(1+z)^n, n \in \mathbb{N} $$ in the Complex Plane Yadeta, Hailu Bikila Complex Variables We study the spatial distribution of the positive, negative and non-real complex roots $z_n $ of the sequence the $(n+1)$th degree polynomial equation $$ z^{n+1}=(1+z)^n,\quad n \in \mathbb{N}.$$ We establish asymptotic approximations to the sequence of the negative, the positive and the non-real complex roots of the equation as $n\rightarrow \infty $. In addition, we discuses the possible areas of applications of the current problem. |
| title | Analysis of the Distribution and Asymptotic Approximations of Roots of the Polynomial Equation $$ z^{n+1}=(1+z)^n, n \in \mathbb{N} $$ in the Complex Plane |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2508.15818 |