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Consider a multivariable power series with positive coefficients such that it is known to converge on a $C^\infty$ (bounded) curve of $\mathbb{R}^n$, where $n$ is the number of variables. In addition, ...

I'm still trying to prove the continuity of a function $u$ which can be interpreted as the restriction of a power series of two variables, which I haven't managed to approach the right way yet. To ...