Weighted Product Inequalities for the Sine Function: A Gamma-Function Approach and Sharp Comparisons
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908964810129408 |
|---|---|
| author | Mahu, Augustine L. Sehba, Benoît F. Williams, Cecilia D. |
| author_facet | Mahu, Augustine L. Sehba, Benoît F. Williams, Cecilia D. |
| contents | Using the log-convexity of the Gamma function and Euler's reflection formula, we give a new proof of a classical weighted sine product inequality. Two different parameter choices yield two competing upper bounds for the same product. We determine precisely, via algebraic criteria, when one bound is sharper than the other. Explicit results are given for the general $n$-angle case, the $2n$-angle case, and for two and three angles. Several sharp corollaries are derived, including $\sin(πx)\leq \sin(2πx(1-x))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13106 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weighted Product Inequalities for the Sine Function: A Gamma-Function Approach and Sharp Comparisons Mahu, Augustine L. Sehba, Benoît F. Williams, Cecilia D. General Mathematics Using the log-convexity of the Gamma function and Euler's reflection formula, we give a new proof of a classical weighted sine product inequality. Two different parameter choices yield two competing upper bounds for the same product. We determine precisely, via algebraic criteria, when one bound is sharper than the other. Explicit results are given for the general $n$-angle case, the $2n$-angle case, and for two and three angles. Several sharp corollaries are derived, including $\sin(πx)\leq \sin(2πx(1-x))$. |
| title | Weighted Product Inequalities for the Sine Function: A Gamma-Function Approach and Sharp Comparisons |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2604.13106 |