Euler-Mascheroni constant
From specialfunctionswiki
The Euler-Mascheroni constant is the number $\gamma$ defined by the formula $$\gamma = \lim_{n \rightarrow \infty} H_n-\log(n) = 0.577215664901532 \ldots,$$ where $H_n$ denotes the $n$th harmonic number.
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
External links
Collection of formulae for Euler's constant g
References
- 1920: Edmund Taylor Whittaker and George Neville Watson: A course of modern analysis ... (previous) ... (next): $\S 12 \cdot 1$
- 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous) ... (next): §1.1 (4)
- 1960: Earl David Rainville: Special Functions ... (previous) ... (next): $7.(1)$
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.32$
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 6.1.3
