We give several integral representation for the Euler- Mascheroni constant using a combinatorial identity for sum_{n=1}^N 1/(n+x)(n+y). The derivation fo this combinatorial identity is done in an elementary way.

The Euler obstruction of a function f can be viewed as a generalization of the Milnor number for functions defined on singular spaces. In this work, using the Euler obstruction of a function, we establish several Lê–Greuel ...

The use of Cauchy's method to prove Euler's well-known formula is an object of many controversies. The purpose of this paper is to prove that Cauchy's method applies for convex polyhedra and not only for them, but also for ...

A fast approximation formula for Euler–Mascheroni’s constant based on a certain integral due to Peter Borwein is given. This asymptotic formula for γ involves harmonic numbers, ln 2 and rational numbers whose denominators ...

A fast approximation formula for Euler–Mascheroni’s constant based on a certain integral due to Peter Borwein is given. This asymptotic formula for γ involves harmonic numbers, ln 2 and rational numbers whose denominators ...

This paper has studied the problem of natural frequencies for Euler-Bernoulli beams having non-uniform crosssection. The numerically-obtained solutions were compared to asymptotic solutions obtained by the WentzelKramers-Brillouin ...

In this work, we present a formula to compute the Euler obstruction of a function f: (X, 0) → (C, 0) and its Brasselet number, where X is a multitoric surface. As an application of this formula, we compute the Euler ...