The gamma function and square-free numbers
Abstract
The gamma function is expressed as an infinite product over the square-free numbers, the terms of which are composed of elementary functions. This formula is shown to be obtainable from the Weierstrass factorisation. It is discussed in relation to other formulae which connect the gamma function with arithmetical functions, and in relation to the Bohr–Mollerup theorem. A brief outline of the history of a few classical formulae is given.
Fields of Study & Subjects
Analytic Number Theory Research
Mathematical functions and polynomials
Advanced Mathematical Identities
Publication details
- Journal / source
- The Mathematical Gazette
- Volume
- 110
- Issue
- 578
- Pages
- 259–273
- Publication date
- 20 January 2026
- Language
- EN