I'm trying to find the inverse function of $$U_{k-1}(\cos(\frac{\pi}{x}))=\sum_{n=0}^{\left\lfloor\frac{k-1}2\right\rfloor}\frac{(-1)^n \Gamma(k-n)}{n!\Gamma(k-2n)} \left(2\cos\left(\frac\pi x\right)\right)^{k-2n-1}$$ When I type it into Wolfram Alpha, it can't figure out the inverse.
I have no idea how to solve this so I would really like to know the solution.
2026-03-25 07:48:37.1774424917
Inverse function of $U_{k-1}(\cos(\frac{\pi}{x}))$?
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