Category:Euler-Mascheroni Constant
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This category contains results about the Euler-Mascheroni constant.
Definitions specific to this category can be found in Definitions/Euler-Mascheroni Constant.
The Euler-Mascheroni constant $\gamma$ is the real number that is defined as:
\(\ds \gamma\) | \(:=\) | \(\ds \lim_{n \mathop \to +\infty} \paren {\sum_{k \mathop = 1}^n \frac 1 k - \int_1^n \frac 1 x \rd x}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \lim_{n \mathop \to +\infty} \paren {H_n - \ln n}\) |
where $\sequence {H_n}$ are the harmonic numbers and $\ln$ is the natural logarithm.
Subcategories
This category has the following 9 subcategories, out of 9 total.
D
- Digamma Function of One Half (3 P)
Pages in category "Euler-Mascheroni Constant"
The following 28 pages are in this category, out of 28 total.
D
- Definite Integral to Infinity of Exponential of -x^2 by Logarithm of x
- Definite Integral to Infinity of Reciprocal of Exponential of x minus One minus Exponential of -x over x
- Derivative of Gamma Function at 1
- Digamma Additive Formula/Corollary
- Digamma Function in terms of General Harmonic Number
- Digamma Function of Five Sixths
- Digamma Function of One
- Digamma Function of One Fourth
- Digamma Function of One Half
- Digamma Function of One Sixth
- Digamma Function of One Third
- Digamma Function of Three Fourths
- Digamma Function of Two Thirds