Is the following result $$\lim_{\lambda \to \infty} \frac{2}{\pi} \int_0^\infty \frac{f(x)}{\sin x} \sin(\lambda x) \, dx = f(0) + 2\sum_{k = 1}^\infty f(k\pi),$$ where $\lambda$ is an odd integer, correct? If so, is it well known? It looks like the Fourier sine transform of $f(x)/\sin x$.
2026-04-02 18:28:22.1775154502
The Fourier sine transform of $f(x)/\sin x$
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