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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gamma]x]/[GAMMA] (1 + x), where [gamma] is Euler's constant and [GAMMA](x) is the gamma function.
1([square root of Zf(Z)]) indicates first-order second class modified Bessel function, dimensionless; "[gamma] indicates Euler's constant, [gamma] = 1-78 ; Z' indicates the Laplace transform variable based on [t.
This is called a harmonic series and it can be shown that the sum is of the order: n(ln(n) + Y) (where Y = Euler's constant = 0.
Euler's constant 1/(lim(x-->infinity) Euler's constant ((1-(1/x))^x)) W^(k/S) Euler's constant [W=number of microstates; k=Boltzmann constant; S=entropy] F/[N.
Mortici, Optimizing the rate of convergence in some new classes of sequences convergent to Euler's constant, Anal.
Some third of the material is concerned with biographical and other contextual issues, while the bulk of the selections focus on particular aspects of Euler's contributions to mathematics, including infinite series, the zeta functions, Euler's constant, differentials, multiple integrals, the calculus of variations, the pentagonal number theorem, quadratic reciprocity, and the fundamental theorem of algebra.
denotes the Euler's constant, which is equivalent to [[[GAMMA](1 + x)].
gamma] is the Euler's constant, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes the product over all primes.
where C is a computable constant, [gamma] denotes the Euler's constant.
Keywords Inequality; Polygamma function; Harmonic sequence; Euler's constant.
where A, B are computable constants, [gamma] is the Euler's constant.