Suppose we know how to evaluate the following integral $$\int_0^{2\pi} f(x,\theta)e^{in\theta}\ d\theta=g(n, x).$$
Is there a general technique to evaluate/estimate
$$\int_0^{2\pi} f(x,\theta)e^{i(h(\theta)+n\theta)}\ d\theta$$
for $h(\theta) = -2\arctan(\sin\theta/(1-\cos\theta))$ for example?
2026-03-26 21:25:54.1774560354
Evaluation of variants of Fourier coefficient
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