New Gamma-based proof of weighted sine product inequalities with algebraic criteria to decide which of two bounds is sharper, plus explicit n-angle results and corollaries like sin(πx) ≤ sin(2πx(1-x)).
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Weighted Product Inequalities for the Sine Function: A Gamma-Function Approach and Sharp Comparisons
New Gamma-based proof of weighted sine product inequalities with algebraic criteria to decide which of two bounds is sharper, plus explicit n-angle results and corollaries like sin(πx) ≤ sin(2πx(1-x)).