Definition

Euler's constant (gamma or the Euler-Mascheroni constant)

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Euler's constant, sometimes called gamma or the Euler-Mascheroni constant, has the mathematical value of .577215664901532860606512090082...(like pi, this constant is an unresolvably long number).

Euler's constant is not as well-known as pi or e , but it is nevertheless significant, especially in number theory and in certain engineering-related formulas and calculations.

Euler's constant (gamma) is defined as the limit of the expression (1 + 1/2 + 1/3 + 1/4 + ... + 1/ n ) - ln ( n ), as n approaches infinity . The abbreviation ln stands for natural logarithm , also called the base- e logarithm. The value of Euler's constant has been calculated to more than 1,000,000 decimal places, and is often approximated to 0.577216.

Also see the Table of Physical Constants .

This was last updated in March 2011
Posted by: Margaret Rouse

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