Difference between revisions of "Euler-Mascheroni constant"
From specialfunctionswiki
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[[Meissel-Mertens constant]] | [[Meissel-Mertens constant]] | ||
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| + | [http://numbers.computation.free.fr/Constants/Gamma/gammaFormulas.html Collection of formulae for Euler's constant g]<br /> | ||
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Revision as of 00:27, 20 August 2016
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
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: 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
