Let $a_k(y)$ be a collection of functions. Suppose that $f_y(x) = \sum_{0}^\infty a_k(y) x^k$ has radius of convergence $R(y)>0$ for some fixed $y$. Are there conditions on the $a_k$ which ensure that $R$ is continuous in some neighborhood of $y$?
2026-04-03 10:09:58.1775210998
Radius of convergence continuous in coefficients
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