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+---- Thread: Collection of formulae for Euler’s constant γ (/showthread.php?tid=447)
Collection of formulae for Euler’s constant γ - mklabgr - 06-17-2026
Summary
This paper is a comprehensive collection of formulas for the Euler–Mascheroni constant ( \gamma \approx 0.57721 ), presenting many ways to define, compute, and study this important mathematical constant. It surveys numerous integral representations, infinite series expansions, and rapidly convergent formulas involving the Riemann zeta function, harmonic numbers, and other special functions.
The authors also explore deep connections between ( \gamma ) and prime numbers through Mertens’ formulas and the von Mangoldt function, showing how Euler’s constant appears naturally in analytic number theory. The collection serves both as a reference and as a source of efficient computational methods for evaluating ( \gamma ) to high precision.
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