EulerGamma¶

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description¶

EulerGamma
    is Euler's constant gamma, with numerical value ~= 0.5772156649.
EulerGamma is the Euler-Mascheroni constant, the limit of
HarmonicNumber[n] - Log[n] as n -> Infinity. It is a mathematical
constant: it has attributes Constant and Protected, NumericQ[EulerGamma]
is True, and D[EulerGamma, x] is 0. N[EulerGamma, prec] evaluates it to
any precision.

Examples¶

No verified examples yet for this function.

Implementation notes¶

Attributes Constant, Protected. `Attributes[EulerGamma] = {Constant,

Attributes: Constant, Protected.

Implementation status¶

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References¶

Source: src/info.c
Specification: docs/spec/builtins/mathematical-constants.md

Notes & additional examples¶

Worked examples¶

In[1]:= N[EulerGamma]
Out[1]= 0.577216

In[1]:= N[EulerGamma, 50]
Out[1]= 0.577215664901532860606512090082402431042159335939923

In[1]:= D[EulerGamma, x]
Out[1]= 0

In[2]:= NumericQ[EulerGamma]
Out[2]= True

In[1]:= N[Gamma[1/2] + EulerGamma, 30]
Out[1]= 2.349669515807048887904679573425

Notes¶

EulerGamma is the Euler-Mascheroni constant, the limit of HarmonicNumber[n] - Log[n]. It carries the Constant and Protected attributes, so it is NumericQ and differentiates to 0, yet stays exact until N[EulerGamma, prec] evaluates it to any requested precision via MPFR.