DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-31

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 Euler-Mascheroni constant

Definition

The Euler-Mascheroni constant is

γ : = \lim_{N \to \infty} (\sum_{n = 1}^{N} \frac{1}{n} - \log N),

provided the limit exists.

Remarks

The next item proves existence and gives the sharper quantitative estimate needed later on this page.

Depends on

The natural logarithm as the inverse of the exponential function

Used by

The harmonic sum is log x plus gamma plus O(1/x) Lemma

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Tom Sanders, Topics in Analytic Number Theory, Chapter 1 (standard reference, not scraped)
Karl-Dieter Crisman, Number Theory: In Context and Interactive (standard reference, not scraped)