DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 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.

The Hankel contour and the principal power branch

Definition

The Hankel contour $H$ is the standard negatively cut contour: it runs from $+ \infty$ along the lower side of the negative real axis to a small circle about $0$ , traverses that circle counterclockwise, and returns to $+ \infty$ along the upper side of the negative real axis.

On $C ∖ (- \infty, 0]$ , the principal logarithm is the branch $Log t$ with $- π < \arg t < π$ , and the associated principal power is

$t^{- z} : = \exp (- z Log t) .$

This is the branch used in the Hankel representation formula below.

Used by

Hankel's representation for reciprocal Gamma Theorem

Dependency tree · 0 levels

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

Sources

K. Chandrasekharan, Lectures on the Riemann Zeta-Function, Lecture 6 §2 (standard reference, not scraped)