 Weierstrass product for the reciprocal gamma function

ID: weierstrass-product-for-the-reciprocal-gamma-function

Codex  0 Created 2026-09-24 Updated 2026-10-14

The reciprocal gamma function has the entire-product representation

\frac{1}{Γ ( z )} = z e^{γ z} \prod_{k = 1}^{\infty} (1 + \frac{z}{k}) e^{- z / k} .

This is a particular application of the Weierstrass factorization theorem.

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