It's easy to construct an entire function of order $\frac{p}{q}$ for any positive integers $p,q$. But is there an example of an entire function of irrational order ($\sqrt2$ for example)?
2026-03-27 03:57:46.1774583866
An entire function of irrational order
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$$f(x)=\prod _{i=1}^{\infty }x^{10^{-i}}$$
You can always generate things , till you have $\infty$ in your hand :-)