structural:expansion, information:extraction
Order ρ

For arbitrary positive numbers ρ {\displaystyle \rho } and σ {\displaystyle \sigma } one can construct an example of an entire function of order ρ {\displaystyle \rho } and type σ {\displaystyle \sigma } using:

f (z) = ∑ n = 1 ∞ (e ρ σ n) n ρ z n {\displaystyle f(z)=\sum _{n=1}^{\infty }\left({\frac {e\rho \sigma }{n}}\right)^{\frac {n}{\rho }}z^{n}}