= Order of an entire function
{title2=$\rho_f=\limsup_{R\to\infty}\log\log M_f(R)/\log R$}
For a nonconstant <entire function>, put $M_f(R)=\max_{|s|\leq R}|f(s)|$. Its order measures the exponent in its exponential growth. Bounds $\log M_f(R)=O(R\log R)$ imply order at most one; a matching lower bound along the positive real axis proves order exactly one. This distinction is stronger than mere entire analyticity and controls the genus in <Hadamard factorization>.
// Target: analytic-number-theory.bigb
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