I have a simple direct question that I am not able to solve. Does the family of complex-valued functions of real variable $x$: $$g_t(x)=(t+ix)^{-\beta}, \beta>0$$ converge uniformly (w.r.t. x) when $t\to 0^+$?
2026-05-14 16:14:14.1778775254
Uniform convergence of $(t+ix)^{-\beta}$
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