What values of $x$ does the sum of this type: $$\sum_{n=0}^\infty \frac{x^n}{n\#}$$
converge for? (where $n\#$ is the product of all primes less or equal to $n$)
2025-01-13 05:11:26.1736745086
The primorial version of $e^x$
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Since $\ln p_n\#\sim n\ln n\sim p_n$, $\ln n\#\sim n$ and $\ln\left|\frac{x^n}{n\#}\right|=n\ln|x|-\ln n\#\sim n(\ln|x|-1)$. This implies the radius of convergence of your series is $e$.