Euler-Mascheroni constant
From specialfunctionswiki
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...
- the hyperbolic cosine integral
- the Barnes G function
See Also
References
- 1920: Edmund Taylor Whittaker and George Neville Watson: A course of modern analysis ... (previous) ... (next): $\S 12 \cdot 1$
- 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): §1.1 (4)
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 6.1.3
