Euler-Mascheroni constant

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The Euler-Mascheroni constant is the number $\gamma$ defined by the formula $$\gamma = \lim_{m \rightarrow \infty} 1 + \dfrac{1}{2} + \ldots + \dfrac{1}{m}-\log(m) = 0.577215664901532 \ldots.$$

Properties

The Euler-Mascheroni constant exists
Reciprocal gamma written as an infinite product
Exponential integral Ei series

Further properties

The Euler-Mascheroni constant appears in the definition of...

  1. the hyperbolic cosine integral
  2. the Barnes G function

See Also

Meissel-Mertens constant

External links

Collection of formulae for Euler's constant g

References