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.

Weierstrass elementary factors

For an integer $p \geq 0$ , the $p$ th Weierstrass elementary factor is

$E_{p} (w) : = (1 - w) \exp ⁣ (w + \frac{w^{2}}{2} + \dots + \frac{w^{p}}{p}) .$

For $p = 0$ the empty sum in the exponential is interpreted as $0$ , so $E_{0} (w) = 1 - w$ .

Used by

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