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
= 0.557) where n is the number of stickers required to collect.
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.sub.A] Elementary charge [F=Faraday constant; NA Avogadro constant] 1.6022*(10^-19)(C) Elementary charge F ma Force [m=mass; a=acceleration] v Frequency of a wave [v=frequency] v/lambda] Frequency of a wave [v=velocity; [lambda]=wavelength] c/[lambda] Frequency of a wave in a vacuum [c=speed of light; [lambda]=wavelength] E/h Frequency of a wave [E=energy; h=Planck's constant] e[N.sub.A] Faraday constant [[N.sub.A]=Avogadro constant; e=elementary charge] 96485.3365 ...
Mortici, Optimizing the rate of convergence in some new classes of sequences convergent to Euler's constant
Sandor, Double integrals for Euler's constant
and ln 4/[pi] and an analog of Hadjicosta's formula.
The second number, known as "Euler's constant
" and always denoted by [gamma] (Greek gamma), turned up in Euler's explorations of logarithms during his early St.
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.
We note that the function on the left-hand side of (1) is equal to [e.sup.-[gamma]x]/[GAMMA] (1 + x), where [gamma] is Euler's constant
and [GAMMA](x) is the gamma function.
Sintamarian, A generalization of Euler's constant
denotes the Euler's constant
, which is equivalent to [[[GAMMA](1 + x)].sup.1/x]/[x.sup.1-[gamma]] being increasing on (1, [infinity]).
[gamma] is the Euler's constant
, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes the product over all primes.
As an application, we give the upper and lower bounds for the expression [n.summation over (k=1)] 1/k - 1n n - [gamma] = 0.57721 x x x is the Euler's constant
where [gamma] is the Euler's constant
. Now combining the Stirling Formula (see reference ), we can get