On the constant in the Mertens product for arithmetic progressions. I. Identities

TL;DR

This paper establishes new mathematical identities for the constant in the Mertens product for arithmetic progressions, advancing theoretical understanding of these constants.

Contribution

It introduces novel identities for the Mertens product constants in arithmetic progressions, providing a foundation for improved numerical computation.

Findings

Derived new identities for the constants

Enhanced theoretical framework for Mertens products

Set the stage for future numerical analysis

Abstract

The aim of the paper is the proof of new identities for the constant in the Mertens product for arithmetic progressions. We deal with the problem of the numerical computation of these constants in another paper.