Pairs of lattice paths and positive trigonometric sums
Victor J. W. Guo, Jiang Zeng
TL;DR
This paper extends previous results on the positivity of certain trigonometric polynomials by replacing binomial coefficients with products of two binomial coefficients, providing new proofs and generalizations.
Contribution
It introduces a novel approach to proving positivity of trigonometric sums using products of binomial coefficients instead of single binomial coefficients.
Findings
Proved positivity of new classes of trigonometric polynomials
Extended previous binomial coefficient results to product forms
Provided new proofs and generalizations
Abstract
Ismail et al. (Constr. Approx. {\bf 15} (1999) 69--81) proved the positivity of some trigonometric polynomials with single binomial coefficients. In this paper, we prove some similar results by replacing the binomial coefficients with products of two binomial coefficients.
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