Note on an Acoustical Constant

A Note on Artin’s Constant

P p(pi−1) , where the summation is over first N prime pi, k ∈ Z+. The classical summation formula is as follows: A = limN→∞Σ(N), where Σ(N) = 1 N ∑ φ(pi−1) pi−1 . The changes needed for arbitrary g are addressed in Theorem 1, a good exercise in basic analytic and algebraic number theory. The same procedure can be applied to other number-theoretic constants like A (see, e.g., [Ni]). In Theorem 2...

A note on a curious formula for Euler’s constant

In this short note we will use the residue theorem to establish a formula for Euler’s constant. In particular, we offer a slightly generalized version of an interesting infinite series due to Flajolet, Gourdon, and Dumas. 1 Properties of γ Recall that γ is usually defined in terms of the partial sums of the harmonic series: γ := lim n→∞ 

Note on thermodynamic fermion loop under constant magnetic field

The one-loop effective potential of a thermodynamic fermion loop under constant magnetic field is studied. As expected, it can be interpreted literally as a dis-cretized sum of (D−2)-dimensional energy density above the Dirac sea. Large/small mass expansions of the potential are also examined.

A note on Constant - RoundZero - Knowledge Proofs for NPAlon

A Note on Constant-Free A Posteriori Error Estimates

In this note we look at constant-free a posteriori error estimates from a different perspective. We show that they can be interpreted as an alternative way of expressing the residual of a finite element approximation and thus fit into the same framework as other a posteriori error estimates such as residual error indicators. Our approach also reveals that, when applied to singularly perturbed r...