A Survey of Euler's Constant

  The mathematical constant γ, which is known as Euler's constant, is not as well known as its cousins π, e, i, but is still important enough to warrant serious consideration in the circles of applied mathematics, calculus, and number theory. Some authors will occasionally refer to γ as the Eul...

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Bibliographic Details
Published in:Mathematics magazine 2009-10, Vol.82 (4), p.255-265
Main Authors: Dence, Thomas P., Dence, Joseph B.
Format: Magazinearticle
Language:English
Subjects:
Approximation
Calculus
Eulers constant
Harmonic series
Integers
Mathematical constants
Mathematical functions
Mathematical integrals
Mathematics education
Number theory
Numbers
Prime numbers
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Summary:  The mathematical constant γ, which is known as Euler's constant, is not as well known as its cousins π, e, i, but is still important enough to warrant serious consideration in the circles of applied mathematics, calculus, and number theory. Some authors will occasionally refer to γ as the Euler-Mascheroni constant, so named after the Italian geometer Lorenzo Mascheroni (1750-1800), who actually introduced the symbol γ for the constant and also computed, though with error, the first 32 digits. Sometimes one will find in older texts the symbols C (this was Euler's constant of integration) and A (also from Mascheroni) to represent the constant, but these notations seem to have disappeared in the modem era. Here, Dence and Dence present a survey of γ that is both manageable by, and enlightening to, those who favor mathematics at the undergraduate level.
ISSN:0025-570X
1930-0980
DOI:10.4169/193009809X468689