DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-08-29

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

The order of an entire function

Definition

Let $f$ be entire and put

$M_{f} (r) : = \max_{∣ z ∣ = r} ∣ f (z) ∣ (r > 0) .$

The order of $f$ is

$ρ (f) : = {lim sup}_{r \to \infty} \frac{\log \log M_{f} (r)}{\log r},$

with the convention that a constant nonzero entire function has order $0$ and the zero function is left outside this definition unless stated otherwise.

Used by

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Elias M. Stein and Rami Shakarchi, Complex Analysis, Ch. 5 Functions of finite order (standard reference, not scraped)