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A term for a unimodal function similar to $\exp(-x^2)$

Is there a term for a smooth $\mathbb R\to\mathbb R^+$ function that is unimodal (has one local maximum), and whose $n^{\text{th}}$ derivative has $(n+1)$ local extrema? An example of such a function is $\exp(-x^2)$. An example of a unimodal function that does not fit these criteria is $\frac1{1+x^4}$.