I am given the Bessel function of first kind of order $n$, $$J_n(\beta)= \frac{1}{\pi} \int_{0}^\pi \cos(\beta \sin x-nx)dx.$$ $n$ is positive integer. It's value is known as $J_n(\beta)\geq0.01$ for a particular $\beta$, meaning I need to find out the maximum $n$ for which the function doesn't fall below $0.01$. How can I determine the order $n$ from this?
2026-04-03 12:44:56.1775220296
Calculate order from given value of Bessel Function of first kind
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