The Bohr-Mollerup Theorem characterizes the gamma function as the unique function on the positive real numbers that is logarithmically convex, satisfies the functional equation relating its value at x plus one to x times its value at x, and equals one at x equals one. Named for Harald Bohr and Johannes Mollerup, it gives the cleanest axiomatic justification for treating the gamma function as the natural extension of the factorial.
Facts
StatementThe Bohr-Mollerup theorem states that the gamma function is the only function on the positive real numbers equal to one at one, satisfying the same recurrence as the factorial, and logarithmically convex, so those three properties alone determine it uniquely. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Bohr-Mollerup Theorem (Wikipedia)
Sources
1. Bohr-Mollerup Theorem (Wikipedia)
Wikimedia Foundationlead paragraph, first sentence
In mathematical analysis, the Bohr-Mollerup theorem is a theorem proved by the Danish mathematicians Harald Bohr and Johannes Mollerup.
- In Branch: Analysis, Lead sentence
View the Source 2. Gamma Function (Wikipedia)
Wikimedia FoundationHistory section, paragraph on the gamma function characterizationQuote, History section, paragraph on the gamma function characterization
A definite and generally applicable characterization of the gamma function was not given until 1922.
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