Euler's Constant

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Euler's constant

[′ȯi·lərz ¦kän·stənt]
(mathematics)
The limit as n approaches infinity, of 1 + 1/2 + 1/3 + ⋯ + 1/ n- ln n, equal to approximately 0.5772. Denoted γ. Also known as Mascheroni's constant.

Euler’s Constant

 

(or Mascheroni’s constant), the limit

which was considered by L. Euler in 1740. Euler gave a number of representations for C in the form of series and integrals; for example,

where ζ(s) is the zeta function. Euler’s constant is encountered in the theory of various classes of special functions, such as the gamma function. It remains unknown whether Euler’s constant is an irrational number.

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References in periodicals archive ?
2], [gamma] is the Euler constant, and [summation over (p)] denotes the summation over all primes.
p] denotes the summation over all primes, and [gamma] be the Euler constant.
p]p (ln(1-1/p) + 1/p - 1], [gamma] be the Euler constant.
where [gamma] is the Euler constant, [epsilon] denotes any fixed positive number.
where c is a constant which depends on q and l, [gamma] is the Euler constant.
where [gamma] is the Euler constant, " denotes any fixed positive number.
1] 1/p) + 1/p), [gamma] is the Euler constant, a and b are two computable
4], C is Euler constant, d(n) be the Dirichlet divisor function.
where A = [gamma] + [summation over (p)](log(1 - [1/p]) + [1/p]) + [summation over (p)] [1/[p(p -1)]], [gamma] is the Euler constant.
Sandor, On generalized Euler constants and Schlomilch-Lemonnier type inequalities, J.