An entire function f is said to be of finite order if there exist numbers a, r>0 such that left bracketing bar f(z) right bracketing bar <=exp(( left bracketing bar z right bracketing bar )^a) for all left bracketing bar z right bracketing bar >r. The infimum of all numbers a for which this inequality holds is called the function order of f, denoted λ = λ(f).

entire function | function order