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Let $n$ be even and consider the discrete sine transform of type 5 which is the matrix $$S=\left(\sin(k+1)(l+1)\frac{\pi}{n+\frac12}\right)_{k,l=0}^{n-1}$$ Let us denote by $s_{-,l}$ the $l^{\text{...

Let $f:R\rightarrow R$ be a continuous function which satisfies the Zygmund condition $$ |f(x+\delta)+f(x-\delta)-2f(x)|\leq \text{const} \frac{|\delta|}{(\log\frac{1}{|\delta|})^{\alpha}}, \,\, \...

Cross-post from MSE. The Jacobi-Anger expansion gives expressions for functional iterates of trigonometric functions in terms of Bessel functions. For instance, we have $$\sin(z \sin(\theta)) = 2 \...