ExampleConstruction: Literature-sourcedVerification: AI-generatedprecheck passaudited 2026-08-30

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.

Half-integer and negative-half-integer values of Gamma

Example

$Γ (3 / 2) = \frac{\sqrt{π}}{2}, Γ (5 / 2) = \frac{3 \sqrt{π}}{4}, Γ (- 1 / 2) = - 2 \sqrt{π} .$

Facts & Assumptions

Given: $Γ (1 / 2) = \sqrt{π}$ and the functional equation.

[L1]

$Γ (1 / 2) = \sqrt{π}$ (The value of Gamma at one half).

[L2]

$Γ (z + 1) = z Γ (z)$ (The Gamma functional equation).

Verification

technique · direct

1.1

Applying [L2] at $z = 1 / 2$ and $z = 3 / 2$ gives $Γ (3 / 2) = \frac{1}{2} Γ (1 / 2)$ and $Γ (5 / 2) = \frac{3}{2} Γ (3 / 2)$ .

L2given

2.1

Applying [L2] at $z = - 1 / 2$ gives $Γ (1 / 2) = (- 1 / 2) Γ (- 1 / 2)$ . Substituting [L1] into step 1.1 and this last identity yields the three displayed values.

step 1.1L1L2algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

8 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

K. Chandrasekharan, Lectures on the Riemann Zeta-Function, Lecture 6 §1(vii) (standard reference, not scraped)