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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.07613 |
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| _version_ | 1866910911440093184 |
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| author | Ren, Changyu |
| author_facet | Ren, Changyu |
| contents | In this paper, we extend the classical Newton-Maclaurin inequalities to functions $S_{k;s}(x)=E_k(x)+\dsum_{i=1}^s \al_i E_{k-i}(x)$, which are formed by linear combinations of multiple basic symmetric mean. We proved that when the coefficients $\al_1,\al_2,\cdots,\al_s$ satisfy the condition that the polynomial $$t^s+\al_1 t^{s-1}+\al_2 t^{s-2}+\cdots+\al_s $$ has only real roots, the Newton-Maclaurin type inequalities hold for $S_{k;s}(x)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07613 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A general form of Newton-Maclaurin type inequalities Ren, Changyu Classical Analysis and ODEs In this paper, we extend the classical Newton-Maclaurin inequalities to functions $S_{k;s}(x)=E_k(x)+\dsum_{i=1}^s \al_i E_{k-i}(x)$, which are formed by linear combinations of multiple basic symmetric mean. We proved that when the coefficients $\al_1,\al_2,\cdots,\al_s$ satisfy the condition that the polynomial $$t^s+\al_1 t^{s-1}+\al_2 t^{s-2}+\cdots+\al_s $$ has only real roots, the Newton-Maclaurin type inequalities hold for $S_{k;s}(x)$. |
| title | A general form of Newton-Maclaurin type inequalities |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2501.07613 |